how many games a day?

I dont know, whatever works with you. For longer time controls, I prefer 15/10, never feel short on time. Despite that I have kind of just been playing blitz and been happy (10 min)

I don't think it's really about the quantity, but the quality of the games. It's easy to play 50+ games every day, if you play bullet. How much will you learn from these 50 games? Probably nothing at all. Why? Because you don't have time to think for your moves, nor analyze why certain moves you played were good or bad. So you just keep making moves, but after the games are over, you can't even recall what happened in most of the games.

Play one longer time control game where you really think about every move, I'm sure you'll remember the mistakes you make and learn from them. I don't really recall any of my bullet or blitz games, but I can think of many different rapid games I played, and the ideas I had in them (and whether they worked or not).

I think 1-3 rapid games a day on average is enough to learn rather fast, if you just analyze the games afterwards trying to think what you did correctly and what were the mistakes.

When I was playing over-the-board chess at/for my local club I would probably average about 3-4(?) games per week (counting 'friendlies') 

I know