The answer to the first three is "yes" (but remember to buy from Windows Store, I don't know whether Play Anywhere applies to buying a physical copy).
Regarding different editions, it all depends how much you're willing to spend and how much content you want. The base game has plenty of content and bear in mind Ultimate still doesn't get you everything since there's a separate expansion pass. However, you'll get a discount on that if you get the Ultimate. It's the most expensive game I've ever played;p
Ultimate gets you VIP, two car packs and a car pass till March 2017, so you'll get an additional 42 cars (seven of which have already been released).
I went with the Ultimate because I was able to grab a couple of cheaper Live pre-paid cards and the difference between Deluxe and Ultimate wasn't so big (wanted the VIP).
The PC version doesn't run perfectly for me, though, and it doesn't always look amazing so it's a good thing you've got an XBox.
Good game but I slightly regret getting the Ultimate.
EDIT: Remember you can usually buy additional cars separately if you're unsure whether you want all of them enough to splash out for the Ultimate.