There is a high probability of stringing, I think.

I tried to print the black keys with 20% infill, but they broke when I was assembling the pieces. So, I decided to print it with 100% infill, and it worked. The black keys base is slightly bigger than the white keys, to resemble the felt between the keys and the piano body. It can be printed in red if you want, just the first 1.5mm.

Slowly fit the parts by pressing the sides, alternately, 'till all the keys come together. I don't think you'll need glue, but you can use it.