Problem developing App using Xcode
In short, Apple want you to play their game - if you're going to participate, you have to play by their current rules, not last season's.
So, no, if you want the latest Xcode you need the OS that supports it.

Your workaround would be to set up a dual boot or VM.

Your second question has a similar answer, well covered here - Can I install any iOS version I wish by picking and choosing which firmware to restore?

You might have a week or so to downgrade before it's blocked, though you'll have to set up as new &amp; lose any backup.