yes, I use home assistant cause I don't need any cloud based stuff for it to work, though I did have to buy a raspi and a zigbee stick to run it on (or if you have some extra hardware laying about, I just like having it separated from my other stuff). I have a few cloud based things attached to it, but I'm selective and don't buy things where essential functionality requires it, but it's a extra & optional feature on something I was going to buy anyways (and that I don't care if data is shared on, like my automatic litter box dump box being full).

You need a ZigBee hub, but it doesn't have to be a Hue one.

You need a coordinator talking to the zigbee bulbs, in most cases this is a usb-dongle for $20-50. Zigbee2mqtt has a great list of different dongles and their pros/cons. The other functionality of a propriatary hub will be fulfilled by home assistant or Zigbee2mqtt+nodered.

Yes but there are USB Zigbee dangles that will serve this need. You don't need another box and power supply, there are multiple brands to choose from, and no cloud account or goddamn SMS confirmation needed.