You raise a lot of points here, I recommend you join the community room in the app, you'll get every detail from the developers there.

they haven't opensourced it yet, but they say they will do so, and they have done so with all the components that keet is built on top of. So given that track record, I think it's just a matter of when.

I asked a developer about the dht, in this context a "server" is just a dht node that you can connect to with its public key (but agree it's confusing they use the same word). the wording might be confusing, but its definitively not what anyone understands as a server in a centralized network https://en.m.wikipedia.org/wiki/Distributed_hash_table

as i've understood, all push notifications on android has to pass through googles servers (but they are encrypted)

and they don't need a server to check for duplicates in usernames

so I recommend you continue to explore and ask around in the chat rooms, figure out if this is for you!