I suggest you up the difficulty level to "Painfull" (or probably "Crippling" from your description of your experiences to date.) At Crippling you start to "earn your money", and the game is far less forgiving of inefficient gamer strategies. The top three levels you will really get into hassles, but do a few Crippling ones first.
Not ignoring the rest of your list, its just that until you have played at a level commensurate with your current ability, its hard to comment meaningfully, you would just get banal generalities. Once you've hit a level that you get repeatedly vapourised on, back off one level, then settle down to work on Strategies.
- I play on Painful with TA (used to be Crippling on DA, but backed off a level, the TA AI is much improved)
- Map size DA Gigantic, map size TA Immense.
- Check mark "yes" to max CPU for all AIs, that gives them the best chance of giving you a hard time as they have more "thinking power". If the PC splutters a bit, uncheck it
- I Always play sandbox, abundant all, very fast tech, no mega events(I hate those things

)
- Bigger ships etc - the smaller the map, the quicker you finish and the less likely you get to the later techs, crude but broadly true. If you want to guarantee 100% all the later techs, play very fast tech, and if still a bit short increase map size to gigantic.
Normal is far too low, its a very forgiving game at that level, hence the easy wins you had.
Also concentrate a little on the opening setup screens, there are lots of options that change the whole character of the game, dont be too hasty to hit "next", read through the screens a little more, there's a few gems lurking there depending on your personal preferences of game style.
Once you found the level you get zapped at, and have backed off one level, I suspect your question list will have changed markedly, hence the importance of finding the right level first, before hitting strategy/configuration detail.
Last but no means least, the game is all about the Economy, its absolutley crucial to really wrap your head around how it works. Unless you really get the economy right you will forever be firefighting, and will not enjoy it in the long run. There are Zillions of threads about the economy on the Forum, particularly in the "Strategies" section.
Regards
Zy