I'm going to try getting an F-Droid build out today, but we've got some build issues with the fdroidserver. In any case - it will get to F-Droid real-soon-now.
I believe so. crankycoder1975 was asking for some pointers on #fdroid irc a few hours back to help build 1.0 for F-Droid. Hopefully any issues will get ironed out. While I appreciate my siblings comment about the app auto-updating - I'd rather have apps managed by a central area (F-Droid on Android, package managers on desktop Linux).
Apparently not from the current latest (0.30.0) version on f-droid. I just went through the MozStumbler menus and did not see anything about (auto-)updating.