Many of the questions you pose will depend on one major factor about which we do not yet have conclusive information: Will, like in most games, areas only be able to contain units of one side? That is, whenever a unit or an army of one side enters a tile occupied by another player, will there be a conclusive battle so that only one side remains? Many games treat tiles like this; but not all. If not -- that is, if tile occupancy is not disjunctive -- that opens up a whole new set of options for combat. For example: Since combat need not be conclusive, because during one time period an army may not totally eliminate the other side, there could be combat rounds during which faster units might attack first; but also combat rounds, in which units with faster weapons might attack first; that is, one could imagine that a combat turn have, for instance, 10 distinct combat phases, in which during the first phase, all piercing weapons get an attack (if a target is in range), the second round, all slashing; the third round, all piercing again; the fourth, all bludgeoning; the fifth, all slashing again; the sixth, arrows; the seventh, all combat spells; the eigth, all area of effect weapons (fire breathing dragons); the ninth, the bludgeoning again; the tenth, all catapults. (It's just an arbitraty example, much like the old AD&D initiative system, just slightly more so.) If your side has no weapons of that type, nothing happens; some of the heavier-hitting weapons might hit harder, just later. Whoever is left alive at the end of those 10 turns, remains in the that square together with the enemy. This might give slightly more raison d'etre to different weapon types. This system works very, very well in the game Star Chamber, for example.
Nevertheless, even if the more traditional type of battle system is chosen -- tile occupancy is disjunctive, hence all battles must be conclusive and fought for how ever many rounds it takes to clear the field, or whatever -- I believe that different weapon types might not be merely gratutious (e.g. more complexity for complexity's sake), but more "fun". Why? Because if implemented with a clever counterpart (armor), there will be more strategic choices available, and the strategic element of reconaissance (spying, scouting, information gathering) becomes more important: Is my opponent utilizing more ranged weapons, more mounted, more siege, more blunt, more slashing, or more piercing? If so, I should research and build accordingly: Armor could come in three main types (you could call it light, medium, or heavy; leather, chain, plate; the nomenclature wouldn't matter), from which players can create "pure" versions (e.g. Valyrian Plate, 100% type 3) or hybrid versions (e.g. Bob's Mounted Knight Armor, 20% Leather, 60% Chain, 20% Plate). Armor mitigates damage by subtracting its value from the damage done to its target; but some armor is better at mitigating an offensive type than another. Chain or Medium armor (or whatever you want to call type 2) should mitigate offensive damage to its full value vs. Slashing (or whatever type 2 attack is called) at 100% of its value, but mitigates piercing at only 30% and bludgeoning at 20%. That is, a pure Chain Mail armor with a AC of 10 should subtract 10 points of damage from every successful slashing attack, but only 2 points of damage from every successful bludgeoning attack. Similar rules apply for Piercing / Light and Bludgeoning / Heavy.
Additionally, you may want to consider how you would like to implement your intuition that faster Mongol-like units should be superior to (unprepared) infantry: do you mean that light mounted troops should have vastly superior strategic map moves through steppe-like terrain? (I believe they should.) Or do you mean that light mounted troops should have vastly superior tactical moves (on the tactical battle grid)? (I believe they should.) Yet if the latter is the case, you need to consider how you want the tactical playing field set up; the little we have seen so far indicates that there is not much room. If an opponent merely spams her field full of infantry, the light Mongols will have no way to maneuver around. How much movement do you want on the tactical field? It seems to me that there might be reason to want to have a LOT more room/movement, if your Mongol horde is to succeed as you believe it should.
Other elements I would like to see included in combat are, in all brevity:
- Armor: Armor should not add HP, but mitigate damage. (This way, some earth spells can explicitly affect armor, while others might do direct HP damage, bypassing armor.)
- Armor Piercing / Double Armor Piercing / Triple AP / Etc: Armor Piercing might be a flag attribute which lowers the damage mitigation armor does by 50%; having double AP does not lower it more than 50%, but merely be effective against Hardened Armor.
- Hardened Armor / Double Hardened Armor / Triple HA / Etc: Hardened armor is tempered to avoid Armor Piercing effects. Armor with the HA flag will disregard the first level of Armor Piercing; if a weapon has Double AP however, it will still cause its armor piercing effect vs. armor and hardened armor, but not Double-hardened armor. A weapon with 4x AP will still only cause 50% armor mitigation reduction, but will do so vs. even Triple Hardened Armor. Scouting your enemy will become very important!
(The law of diminishing returns should apply to this universally: If it takes X resources (time, valuables) to give a weapon the Armor Piercing or a piece of armor the Hardened Armor flag, it should take more to make Double, and more than twice that for Triple.)
- To-Hit: A target's attack value must exceed a target's defense value in order to score a hit. Random factors can / should play a role (no pun intended) here. One could imagine that this random value can be easily modded or even changed in the game setup screen. For example, you might choose at the start of each game: Should the To-Hit calculation be (Attack + d4) - (Defense + d4) >= 0 for a hit, or d6, d10?
- Damage: Melee Damage = (Strength + Weapon bonus) - Armor value.
- Statistics: Ideally, you will want every unit in the game (not only the sovereigns) to have something like strength, dexterity, constitution and willpower values, so that these might become (in a patch, in an expansion, in a mod) affected by spells. Strength is the value added to melee weapon damage, dexterity determines Attack and Defense, Constitution should help determine HP and resistance to poison and possibly fatigue, while Willpower should determined resistance to many types of magic spells and morale. Potions should affect statistics in this way.
- Defense: Should be a value reflecting the units ability to avoid melee blows. Armor should have nothing to do with this. If anything, Armor should have a negative affect on a unit's defense value. (The higher the armor rating, the higher the penalty to Dexterity.) Default might be Defense = (Dexterity + training specialty) - Armor penalty.
- Attack: The ability to score a hit. Default could be Melee Attack = (Dex/2 + Str /2) + training specialty, while Ranged attack might be pure Dexterity.
- HP: HP could be a factor of size and constitution, with additional training to reflect "combat hardiness".
- Injury: A unit which suffers HP damage should not be as effective as a unit which does not. A unit which takes HP damage should have to make morale checks (which it should also do should a leader fall) and have its abilities reduced in relation to the gravity of the wound (5 of 10 HP should be quite serious and should reduce the effectiveness of that unit by more than if it had only taken a 2-HP blow).
- Fatigue: I would like to see fatigue, but would not think it necessary. Anyone who has ever engaged in serious combat sports (I do mixed martial arts at a semi-competetive level) knows that fatigue is *the* single most crippling factor, at least in unarmed hand-to-hand combat. It would be nice to see if performing a combat action (attacking, moving, defending) could cost a certain amount of fatigue points. Ideally (a patch, an expansion) it would be nice to have units be able to have an "Exertion" slider, which would let them "save their energy" by performing tasks at higher energy levels (yielding full damage, full defense values), while they could set the slider to 20% and have their respective values reduced by that amount, but also only suffer a mild fatigue cost.
- Reach: You are not going to have unit types ("Pikemen", "Knights"), but you might want to have something to model the useful paper-scissors-rock effect that these unit types bring. Pikemen are good vs. mounted units precisely because their long but bulky weapons let them "hide" from a fast-moving mounted attack, yet the pike is clumsier once an opponent penetrates the distance. You won't have "pikes", but you could include weapon length: the longer, the slower, but better vs. first attack against an opponent with a shorter weapon.
- Stances/Special Moves: I dont think this absolutely necessary, but nice to have (expansion, patch): A unit could be give various "choices", much like the common D&D RPG menus on the market (ToEE, NWN): act defensively, hide behind shield, all-out attack, feint, usw. -- the more combat research done and applied to that unit in training, the more options that unit has. Conceivably, the different between an elite crack unit and a green unit might be in its number of options. One could consider that some of the "options" be special "combat moves" they could "purchase" in training, which requires both a longer time required to train, a training master in that barracks where the unit was trained, and the prerequisite combat research. One could imagine that a unit could purchase a "jab" (+2 attack, +1 defense) move option, and perhaps later a "riposte" (+2 attack, +6 defense) or a "roundhouse" (+8 attack, +6 damage, -2 defense). Perhaps you want only Leaders / Commanders to have these options, I don't know. Each unit could come with the default move "attack", perhaps. I think your currently implemented "card system" could display this nicely, a little icon on the card for each "move" a unit is capable of. Perhaps combat research has different branches according to different "styles" -- one branch might teach you more of the "Water Dancer" moves (Brad apparently likes R.R. Martin's Song of Ice and Fire series -- imagine these being defensively-oriented moves with large boni to piercing weapons and smaller ones to slashing weapons), while another branch, let's call it Iron Fist, lets you unlock moves which are more offense-oriented and give large boni to bludgeoning and small ones to slashing. This would have the side effect of making research more variable and exciting, as well as adding a nice amount of smaller "milestones". I could imagine a nice pack of 50-100 moves being included in the game (expansion).
- Combat Experience (veteran units who have seen battles): in addition to giving a unit increased morale, attack, and defense values, you might also consider having a mini-upgrade system available, somewhat like CivIV: some units could spend their XP-points on specialties. For most of these specialties, however, you will need "types", since the game does not have a flag for "is a knight" or "is a maceman" or "is an archer" -- this would be another reason to implement a damage type system (piercing, slashing, bludgeoning with its armored counterparts). Experienced units might get a "banner" marker, which means that other units in their squad are less likely to rout. Perhaps combat experience can let a unit purchase one of the above-mentioned "Special Moves", or a portion of one (e.g. "jab" costs 1 experience point, but "hare kajima" costs 5.)
- Unit speed will probably need to be tied in somehow to the amount of resources (not time spent training) a unit is equipped with plus the speed bonus a mount would give; intuitively, a heavily armored infantryman should be slower than a lightly armored one; a heavily armored mounted unit should be slower than a lightly armored one. I think this will be hard to implement, however -- how are you going to distribute the "heavy" attribute to equipment?
Argh, must go, my baby is crying -- will write more later. Sorry so inarticulate