Jisho

That example sentence seems a little unnatural both in Japanese and situations. If one dares to make such a question in （尊敬語）sonkeigo, it could be written this way.

「あの先生は歌うのがお上手かどうかご存じですか？」

@namakemono It's worth noting that in that sentence お上手 would be sonkeigo toward the teacher, but ご存じ would be sonkeigo toward the listener. If sonkeigo was not needed toward the listener, then that part could be kept the same as originally.

Thanks for the help with the language to use.

But it seems there is something else to learn here. It did not occur to me that it might be impolite to ask if sensei might be a skillful singer--at least I think that is what namakemono means. The question comes from an exercise in Genki lesson 20. The other possibilities are as follows:

Do you know if sensei likes tennis?
can speak German?
is interested in politics?
where sensei lives?
what sensei will do this weekend?
what time sensei goes to bed?
what sensei's hobby is?

Are any of these questions OK? Or is it always impolite to ask questions about sensei?

Thanks for your thoughts....

@Streiker
In a strict, official setting, it may be frowned upon to ask such questions. For example, at a music school, it would be considered impolite to ask about the teacher's singing skills. However, seeing the teacher at karaoke would be a different situation.