--

Yes. Perfectly natural English usage.

Yes.

I can't see how this can be a word play. Word plays involve words that sound the same or very similar, or at least rhyme. 'Bother' and 'brother' don't sound anything like each other.

This is a word play on bother/brother. Of course, sister/brother are opposites, creating the discord or word play. I don't fee that it is a "usual" construction, but rather it calls attention to the situation because of the word play and it is somewhat jocular. If you want a "normal" phrase, you would say, "His sister is a real pain in the a**." That's very common.