Will a 255/35/20 fit a 9 and 10 inch rim okay? Is it going to stretch out too much or will be be fine?

The acceptable rim widths are 8.5" to 10". The tire meets its dimensional spec when mounted on a 9" wheel. That is the size I would use. You may have a good reason to use a wider wheel, but don't go over 10".

I dunno much about tire tech but will the overall diameter still be the same if fitted with a 9" or a 10" wide rim?

The diameter should be slightly smaller on a 10".