Yes, the campaigns limit available techs (especially the DL one). Most of them get unlocked the further along you are. In DL, by the time you reach "Apocalypse" you should have all techs, that are available in the campaign, at your disposal, but I'm not entirely sure about this. It's been quite some time since I played the campaigns.

Most of the defense modules for starbases require either Battle Stations or the previous module in their respective tech-line. E.g., Combat Armor I should require Battle Stations, while Combat Armor II should require Combat Armor I. I say "should", because I'm not certain if that is the case here, and I can't verify it by checking the files, because my gaming computer is currently out of commission.

Several prerequisites for starbase modules are bugged and/or don't take into account the tech tree changes made in TotA. This is especially apparent with the defense modules unlocked by the weapons technologies. They all require the module unlocked by the previous tier, but not all of the races have access to all of the necessary techs, which means, that they can't fully upgrade their starbases. (Not that using the defense modules in the un-modded game is that useful anyhow.)

Depends on what you want:

If you are mainly interested in just having the bugs fixed, APT is probably your best bet.

If you also want some balance-changes, while staying as true to the lore of the game as possible, then give my mod, Autumn Twilight, a try. The AI still needs a little work, but it shouldn't be that bad for a beginner.

If you don't care that much about lore-friendliness, and just want the bugs fixed and better balancing, then try Tolmekian's TechTree Fix.

If you primarily want a better AI, along with some bug fixes and better balancing, then give MarvinKosh's Space Weapons Fix Mod a try. However, it may not be for everyone, as it deviates quite heavily from the base game.

One last note: Except for APT, none of the mods are likely to be compatible with the campaigns. Mostly due to changes to the tech trees. Tolmekian's and mine could possibly work in some case (especially the TotA campaign), but MarvinKosh's definitely won't. His changes are just too radical.

Not yet. I'm planning to make my mod compatible with all campaigns, but have to wait until my gaming PC is fixed.

For now, I would recommend the mods only for sandbox-play.