1) Somehow I can never stay logged on to the site neither with Firefox or EI when even I leave the site. I always have to log in manually on the old JU and this new one.
Are you clearing cookies regularly? Do you have any software that does browser file scrubbing for privacy/security reasons?
2) Is this site more Firefox friendly? The quote feature never worked for me.
I've used Firefox 2 and IE in equal measure to test JU2 throughout the development of the site. It should work just fine (note: Firefox 3 Beta has issues)
3) Can I still use programs such as Microsoft Word Blog and Microsoft Live Writer to post articles?
Yes! I will have the new information on that posted this afternoon.
4) Is there a signature feature, I wouldn't mind having something like a modo, a phrase or my name at the bottom of each of my replies. I'll even take a add on for Firefox that can do that.
No signatures at this time. We're considering it for a later update.