for me, NVDA freezes when selecting sources and even I don't know why. (although sometimes my entire screen doesn't get captured when I'm using display capture anyway)
It really isn't. the reason why you probably think that is because you don't even know how to use it. I've used OBS for lots of my content, recordings and streams and such, and I have no problems with it. Maybe try reinstalling it?
like I mentioned earlier the only issue I have is when adding new sources because NVDA will freeze. But if a stream is crashing it may just be your network
My suggestion for the streaming issue is to study the logs to see the real issue when your network is not working or it is slow. OBS shouldn't crash like that; it should just end a stream and maybe pop up with a warning.