Funkwhale is awesome, but it's also one of those FOSS projects whose website doesn't exactly illustrate what it exactly is or what it's exactly for, so here's a direct link to straightforward answers for both of those questions

https://docs.funkwhale.audio/features.html#scope

I want to say +1 for funkwhale, but I didn't get it to work with the subsonic client and haven't found yet a way to download/cache songs from my library on the phone. Have you figured this out?

Subsonic phone clients were kind of a crapshoot last I checked. Ultrasonic was the only one that kinda worked for me.

https://github.com/ultrasonic/ultrasonic

Ahh no I haven't, if that's not working then it might be better to stick with subsonic...