Password request problem: I have my preferences set to check for mail every five minutes, but find that this is preceded by a request for my password. Then, I need to I enable 'Take accounts on line.' before Mail checks. Mail.app does ask for permission to access my keychain and then ignores the stored passwords.
Since upgrading to Snow Leopard on 16th July 2011 I have updated all my apps and utilities, installed all Software Update, ran Disk Utility, Disc Warrior, and Onyx.
The only one of your issues I've run into, and it made me crazy for a while before more or less inexplicably disappearing, is your password issue, which seems to have ultimately been corrected by rerunning whichever OS X Update Combo was most recent at the moment.
I can't begin to interpret your crash report, but regardless, I'll suggest that as your first troubleshooting step you (Edit: install or, as the case may be,) reinstall the
Mac OS X 10.6.8 Update Combo v1.1; the procedure has been known to work "miracles."
Good luck, and please keep us posted.