Well I can't answer all of your question I just don't have the time to play the game anymore. 
However the whole combat system depends on yoiur technology and their technology. Have a huge lead and you can win striaght odds fights. However I always keep my armoured/mechanised and infantry units seperate. Units move at the speed of the slowest unit so putting them together will just hold your fast units back.
I do like AA, but you need to research do some research to make it worth yoru while. If you have high AA values due to research then spending just a little time on upgrading (say 2 or 3 times) can make it a bit costly to bomb you.
However the whole combat system depends on yoiur technology and their technology. Have a huge lead and you can win striaght odds fights. However I always keep my armoured/mechanised and infantry units seperate. Units move at the speed of the slowest unit so putting them together will just hold your fast units back. I do like AA, but you need to research do some research to make it worth yoru while. If you have high AA values due to research then spending just a little time on upgrading (say 2 or 3 times) can make it a bit costly to bomb you.