As someone who still builds boards, both hotswap and solder, my take:
1. Yes, hotswap sockets are still surface-mounted/soldered on the back of PCBs.
2. The design has changed iteratively over the years but largely the same -- precautions generally apply if you're using a hotswap PCB -- you should use two hands, or at least minimal but barely sufficient force in inserting switches into them, making sure pins are lined up and not overforcing the insertion process. The same risk of having sockets pop off from the back exists, since the surface-mount soldering of the sockets is still largely the same as before, even though the integrity of the sockets' inner metal parts themselves has gotten a decent bit better (they do not "fold out" as much as before).
3. The best way to support the sockets from behind, honestly, is to take out your PCB/plate combo outside of the keyboard case, and use two hands. One hand pushing the switch, and the other hand supporting the PCB + corresponding socket from the back. If you won't / can't do that (out of convenience), then the next best thing is to just wiggle as the pins of the switch insert and place themselves relatively easily into the socket.
4. Flex cuts will affect durability in the sense that it's easier to push back and bend portions of the PCB backwards, hence applying shearing forces to the socket joints. Overall, with flex cuts, socket lifetime is probably worse if you're not careful.
5. I can't really say much about brand-based differences, but the two main sockets I've seen are Kailh-made or Gateron-made.
All in all, while personally I don't really think the trouble of soldering + desoldering is all that bad, hotswap PCBs are indeed much more of a norm (with pretty decent compatibility as well), and should be durable if you're moderately careful.
