WOW!!!!! Lots of questions in this....
Yes you can do partial water changes, but be careful, in fact, you probably want to do them rather frequently, just because of the baby fish, I would say twice a week, 10-20 percent each time. Just stay clear of eggs and fry.
As far as food goes, I would use a liquid fry food, or the dry fry food, both are good, but I believe the liquid will do better getting to the fry, the dry tends to stay up top for a while...However, you don't need to worry too much about the fry getting food, because you will probably find the parents chewing up some of their food and spitting towards the fry so they can eat as well
Those are definutely eggs in the picture, I had the same setup in my 55, to include the clay pot
