I just had the “please log in again” problem:
http://wordpress.org/support/topic/169771
For me (using Firefox on Windows), it turned out that the “please log in” window was an IE window and once I had logged in via IE, uploading worked.
I wasn’t having the other uploading issues you’re having, but this might at least be a helpful clue.
Finally got this sorted out, I think.
I decided to try using IE, and the login screen looked familiar: “Please log in again.”
So (for some reason) my “Please log in” window was an IE window.
Once I had logged in via IE, then uploading via Firefox worked.
I don’t understand why things worked this way, but there you go.