1) Press "T". The camera centers on your demigod and follows your moves.
2) I agree. But for me i like to zoom out/in, seems quick and looks very cool...
3) I don't understand what you are referring to. But i have a similar problem: The demigods in your team have the same color (green) as your troops, and it's hard to see where are your team members are, if they stand in the middle of a friendly mob (lol). Either make the creeps other color on the map (like white), or the team demigods.
4) Not a problem for me, i just press Enter and see the log. I don't have to type anything, if i just want to see...
I have more suggestions and bug reports, but i'll make another thread.
Btw, do the people from GPG watch these forums? I thought that Stardock only made the netcode for it...