It is not absolutely incorrect to say 'I play a little piano,' it would probably be better to say: 'I play the piano a little' (so it does not look like you are referring to a piano that is small!). However, that would not necessarily convey the impression that you don't play it well. 'A little' would generally be seen to refer to a time scale, so 'I play the piano a little' would probably give the impression that you don't have much time to play the piano, so only play it when you have time. In this case you would have to add the information that you don't play well, for example: "I play the piano a little, but I'm not very good."

I think so. Also: I can play a little piano. I can play the piano a little bit. Can you the play the piano? I can play a little.