I suggest you use a tool like ecalc.ch to figure it out. There are a ton of variables to get a really useful answer but that tool will let you figure it out.
Yes, but… you also need to consider the temperature and any local weather. So if everything is equal the change in pressure is linear, but in reality it often isn’t so simple. If you’re working at those heights I’m going to assume you’re in some kind of mountainous area and that can come with localized wind and heating/cooling effects that will make the relationship complex.
The props don’t have to be specialized for high altitude, they just need to be a higher pitch than what you would fly at lower altitude. A longer prop may also help. Again, ecalc.ch is your friend.
Unless the board you are using has some special limitation the barometer should work just fine. To be sure, check with your flight controller’s manufacture to be sure they haven’t put a limit. I don’t think I’ve ever noticed one with any of the boards I’ve used. I’d be more worried about temperature issues, especially on batteries and any soft mounting used. Remember in traditional aviation these altitudes are just normal operations.