1. Do they know some old songs?
Yes, they do. They know some old songs.
2. Do they know any old songs?
Yes, they do. They know some old songs.
3. Do they know old songs?
Yes, they do. They know some old songs.
(Which question is grammatical and sutible for the answer?)
All are fine.
All three questions are grammatically correct and suitable for the answer. They are asking about the same thing - whether or not "they" know any old songs. The difference lies in the phrasing and emphasis.
Question 1: "Do they know *some* old songs?" - This question suggests that they know at least a few old songs, but not necessarily a wide variety of them.
Question 2: "Do they know *any* old songs?" - This question suggests that they know at least one old song, but not specifying whether they know more than that.
Question 3: "Do they know *old* songs?" - This question is more general and does not specify any quantity of old songs they may know.
All three questions can be used depending on the context and the desired emphasis.