I'm using firefox and i never had this problem. Although I did have a lot of problems editing listings and getting signed in a day or 2 ago, I assumed just a high server load.
Ebay quite often asks you to sign in to edit a listing if you haven't already entered a password in that session.
Although it remembers who you are from one session to another, it only actually asks you to confirm it when doing something on your account, editing a listing, making a new one etc.
Sorry I can't help you on the dll problem though