Checking multiple mail folders in MobileMail
AFAIK. No.

MobileMe only has push mail enabled for the Inbox itself, and even then it still doesn't support live updating the way Exchange does. Ie. If I delete the email on MobileMe or even in Apple Mail or Outlook, the iPhone doesn't get notified of the change. It will only pick up the change on the next push notification for an incoming mail.

However, they are actively trying to improve the MobileMe platform, so I foresee this becoming possible in the near future.