Haven't used Git or the EGit plugin myself, but I use Eclipse daily as my dev env, with an SVN plugin for source control. As they're both Eclipse Team providers I imagine it's as easy to use - right click > team > commit / right click > team > update to HEAD etc.
Clearing the data worked for me on 1.7 with an Exchange account. Settings > Applications > Manage Applications > All > Email > Clear data. Can't remember if I forced a stop and restarted, but probably worth a go while you're on the screen.