Favor points from achievements count even against the AI. The achievements don't work properly though. You can only get favor for achievments if you manage to get the achievement in one game. So you would have to kill 50 demigods in the first game with your chosen demigod to get the achievement! Easy enough to do if you plan it properly but you probably can't unlock all achievements.
The easiest way to get some favor points fast would probably be to play against your brother though.
I don't think AI games will be counted for stats, at least they shouldn't. The 2 games you got were probably glitches.
