yes and yes.
So far, they have discussed 3 different modes.
1. Single player
2. Multiplayer everyone starts at ground zero, level playing field (literally), and battles their way up.
3. Persistent multiplayer. The results of your multiplayer battles will effect future multiplayer battles in this mode. The details of how (arena control, demigod items, levels, skills, stats, etc)for this mode have not been fully explained.