1) your Demigod is not persistent. you begin every new game with a level 1 demigod. typical matches are quick, they last 15-30 minutes on average. during a match you can earn Favor Points, which are persistent and do last between matches. Favor Points can be used to unlock powerful Favor Items that you can begin play with.
2) pretty decent amount. hard to quantify precisely because i don't have all the data. there are usually several hundred players on at all times, over a thousand at peak times. just guessing though, really.
3) what? uh...yeah, you start at level 1 and gain experience (and level up at certain intervals) to a max of level 20. you gain improved stats and a new skill point to spend with each level up and access to higher level abilities.
4) favor items and player ranking are persistent elements of multiplayer. see item #1
5) the connection problems used to really be that bad. they no longer are. connectivity is now about as good as any other RTS game on the market.
6) the smaller units (reinforcements) spawn automatically from Portal structures on the map if your team controls the Portal. they run along pre-defined paths, you do not control them at all. the reinforcements begin the game largely as fodder and a source of exp and gold to be farmed by DGs. once your team has cleared a path to the enemy Citadel (by knocking down towers and capturing flags) the reinforcements can destroy the enemy Citadel and thus win the game for your team.