'which' should be used if it's a small number to choose from, otherwise 'what' is fine. Grammatically it's good. :) (if you're worried about that 'don't end a sentence with a preposition' rule, that rule is stupid and wrong - your sentence is evidence of that!)

Hi Alexey, or Which/what computer may I connect to? My best, Stephen

Thanks!

yes, that's the correct question. you could also ask "which" computer