1 : How is the AI? Is it hard to exploit (Hmm, AI doesn't attack me in force. Guess I can just turtle forward to win!) or will it adapt to the player? In short, will it be a challenge without it cheating?
Can't say, as the beta AI is not finalized. Stardock games are traditionally known for good AI (which keeps improving with patches), so this probably shouldn't be a major concern.
2: Do we know if AI can be used online, mixed in with people?
All things point to yes.
3: When the online beta was up, how casual was it? RTS online has always stressed me, making it not fun. Playing with friends in SoaSE was extremly fun, because I knew I didn't have to be on the edge of my seat. Playing public games..not quite.
Basically will there be communities that set an occasional game? 16-32 multiplayer sounds like it could be really fun if the people were relaxed.
It's pretty impossible to predict communities before it launches 
It's not an RTS, and turn based games are generally more relaxing to play. That said, because it is a turn based game, don't go into it expecting a sprawling MP community. It may happen, but it's highly likely that a lot of games played will just be comp stomps with friends.
4: Moving into tactical combat : Do we know how it will play out online? Will it be automatic -- will both players (or 1) have to agree to do it manually? Will other players have to view manual battles as well?
Unfortunately, we don't know.
5: Looking at tactical combat stats, they seem open to exploiting (1 stat to rule them all!) or just blandness (jack of all trades, master of none). I don't mean to sound rude. Could a player carve a niche for himself (hmmm, he has really fast units. I should plan/exploit for that) or will players react to most things in the same fashion?
There are more stats and things to take into the account, but the UI just doesn't show them. There are damage types and armor types that have an effect on combat but aren't reflected in the un-finished UI. The balance is also a bit off, as weapons do entirely too much damage compared to HP so most battles early on end up being taking turns one-hit-killing. There's also a unit morale system that's not reflected in the UI at the moment. They also have some improvements in mind for the first couple patches that are too late to get into the game now.
6: During the online beta, how did turns progress? "You have X seconds before the turn ends." "You have X actions to partake in!"
There was no time limit on a turn, but once a player hits End Turn on his client, the others had a certain amount of time to wrap up and hit theirs, else the turn would end automatically when the timer expired. All players go in the same turn, it's not a "Player A's turn, Player B's turn, ..." system.
