VLANs are at layer 2 which is switching. Routing is layer 3.

I have several Unifi switches and a controller (running on an rpi) on my network but I use my own router. I can setup VLAN access ports and trunks all day on the switches no problem, but I can't control the layer 3 routing between those VLANs with the controller, which is what you're talking about. By setting up a gateway/network on each VLAN from my router I can control routing. It's just not as slick as having a USG where it's all controlled via the controller UI.

A couple of their top of the line switches can actually do layer 3 switching. I haven't actually tried that, but the docs don't mention it requiring a USG so I don't think it does.

Yes. As I said, I do that myself with a pfSense firewall/router into Unifi switches and APs with multiple VLANs and routing between them. I've also done it with an Edgerouter + Unifi switches and APs, and a Mikrotik router too. Of course the Unifi controller doesn't control a non-Unifi router, but you can set up whatever VLAN arrangement you want in the Unifi controller and then set up your router to match and do whatever inter-VLAN routing you want separately in its own interface.

It is not all nicely integrated together if you use a separate router (obviously), but it's not like it makes it impossible. It's not even difficult... at least not any more than it would be in any other setup.