Do the hydrogen nuclei from the solar wind combine with oxygen to produce water in the Earth's atmosphere?

No, I do not believe so, because these protons are traveling at 450 kilometers/sec which is far too fast for chemical capture. Also, they are ions which means that if they did manage to get captured by oxygen atoms, you would end up with hydroxyl ( OH ) molecules. The impact would dissociate any free hydrogen molecules ( h2). At least that's my best guess.