My FF sometimes randomly dies when loading a new page or performing some actions in the current one. This time it froze right after I clicked "send" to a very important e-mail. Though when I did the "end task" and started FF again, my Gmail account had that e-mail in the sent folder. Should I worry, or is the fact that it's in that folder absolute proof that my e-mail reached its destination?

It would seem logical to me for the e-mail's code to actually send the message BEFORE copying it into the folder for sent messages. If the person getting this e-mail wouldn't hold it against you to receive the same e-mail twice (ie, they would overlook it being "annoying" (?) or "unprofessional"), it couldn't hurt to copy the message and send it again. Or... you can send another e-mail explaining that you browser crashed and you want to confirm that your e-mail was received.

If there is a chance of FF not sending it, then I'll do this. Thanks again.

Like Moose, I don't think you have anything to worry about, but better safe than sorry.