Couldn't you use HMAC with shared secret key to authenticate messages while keeping plausible deniability? Since the key is only supposed to be known to the 2 parties, the recipient can deduce that a message was actually sent by the sender if he did not create it himself. I think that's what OTR was using.
F-Droid is like package maintainers for Linux distributions. You have to trust them if you want to use their pre-built binary. However, some app builds are reproducible. Check the doc for more info.
DroidFS can open existing volumes. Just click on the "+" button in the bottom right corner, then on the folder icon, and then select the volume directory.
Yes, just create an empty room with only you inside