For what it's worth, everything about signal is open source and you can see how little data they can actually collect from you even if they wanted to. I believe they wouldn't be able to start collecting more data by modifying the server code, because the features which prevent them from receiving your info are built into the protocol and the client apps as well.
But since it is open source I suppose it would be possible to run your own server too... I suspect you just wouldn't be able to talk to the same people if you did (you'd effectively be running your own version of signal and that server would do the necessary coordination tasks for you and the other people using it)
signal-cli lets you register from a computer. If you have a modem in your computer, you can use this to receive the confirmation SMS. A friend also managed to register a landline (I think the phone received a code through a voice message).
They allow usernames as an alternative to sharing your phone number with other people. You still need a phone number (and the phone app) to create and activate an account.
It's very phone-first.