I'd probably choose Qt.
I'd probably choose Qt.
Of course you can. The Common Controls are part of Win32 in the same way that user32 and gdi32 are.
Also worth noting that Microsoft is in the unique position that they do not want to break countless applications and realise that backwards compatibility is their strong point and a major reason why people use Windows, so even if something is "deprecated", unless it's related to some low-level system functionality, chances are it is not going to stop working. I'd say that they use "deprecation" more as a way of marketing newer-but-not-necessarily-better technologies.
On the subject of cross platform I wouldn't go for qt or anything like it unless I really needed it. All those frameworks are too compromised if you are targeting a single platform. Possibly even if you aren't.