As a native UK English speaking IT professional I would select and deselect text, objects and buttons on a computer system. However, being English, I would tick boxes rather than check them , if only to avoid the ambiguity of the verb to check. I'm not sure I could ever bring myself to untick a box, although strangely I'd have less of a problem unchecking one!
I agree that unselect sounds wrong but I have seen it used. Deselect is in M-W unlike unselect.
I think the problem is that none of these negatives has much of an existance outside of the world of IT, so there are few rules. I can't imagine using any of them in a piece of real text. Conversely, if asked, I would say the opposite of select is discard, and you can't use that in this context.