Yes definitely. Beth wyt ti'n wneud? and Beth wyt ti'n gwneud? are both absolutely fine in colloquial language.
It refers back to the question 'what', literally 'what are you it doing', more correct English = "what is it you are doing"
Yes, that's more normal in colloquial language. Including the ei makes it more formal.
People go even further - in rapid speech the same sentence can sound like 'be ti'n neud'
It shouldn't. Report it. The mods are pretty good at keeping on top of things here.