I don't use Thunderbird, but I did have an old copy lying around on my HDD. It's version 0.9, so I'm not sure if things are different for you.
The date/time thing sounds very wierd. It may be a glitch in the program. Perhaps you should try getting a newer (or older) version of the program.
The only other thing I can think of is that maybe you're accidentally clicking one of the little "sort by" buttons when you move the mouse around from message to message. I know I've had that problem with a few different programs. It's a little worse for me because I use a touchpad (and thus can accidentally click a lot more easily than with a regular mouse), but it's always possible that something like that is happening. Given the fact that I don't see a "sort by time" option (and the fact that putting one in really makes no sense), I have a feeling it's more likely to simply be a glitch.
The signature, I can help with. In version 0.9, you can add a signature by going to Tools -> Account Options. In the general options page (first menu item below your username), there's a little checkbox that says something like "Attach this signature to outgoing messages," and a text box below it for you to enter you sig. Unfortunately, it does not appear to support multiple sigs for a single user.
Not sure what to tell you about the attachment thing. I checked with version 0.9, and it didn't do that at all. I know I did have that problem with AOL, back when we were using them as our ISP. I found that sending multiple attachments helped, as did zipping the text files (so it didn't recognize the file as being text). Not the best option for the EIC of the archive, though. Hmm... Does it make any difference if you tell it to search for "All Files" rather than "Text Files" when attaching? Take a poke at the options and account options. I don't see anything in version 0.9, but they may have added something. The only other thing I can suggest is, once again, to try to find a different version.
(You can find all available versions
here. )
Oh, one more thought... Maybe there's a
Thunderbird Extension which will help?
Paul