Well, the Ultimate Edition is basically the same as having the base game and both expansions so you'll be fine with any of the mods.  The only thing is, most of the tech tree mods modify the same files, so you can only play with one of those installed at a time.

Additionally most or all of them change the raceconfig, so if you want to keep your configurations for the default races, you'll need to back them up before changing mods (if not, just hit clear on each race and reconfigure their abilities to your taste before starting a new game).

As for which one to pick, to be fair all I can say is to try them in turn until you find one that you like.  Of course if you find something you don't like about a mod, you can comment on one of the mod posts here on the forums.

I don't know about any of the other mod authors but I plan to keep doing updates right up until I see the whites of GalCiv 3's eyes.

Use the 'External Link' at the top of the page or download using the link labelled 6A from the top post, they're both the same.

All races are already set to use AIP 11 in APT2. No need to change them. 

Could it be, that the AI is broke? That's the only reason I can think of, for why it is no longer researching.

We cannot mod the AI directly. It is hardcoded. The only thing we can do, is trying to influence some of its decisions, like what to research or what improvement to build on its planets.

It depends on the mod, but all fix mods use separate folders, so it is possible with them. After you've installed it, just change the Mod Directory in the Game Options so it points to the new mod.