number of games

No present limit on how many games you can have.  Most of us can only handle a few, but some successfully play hundreds.  I don't buy that playing over a thousand games at once makes any sense but yes, there are folks who do that.

Take a peek at how many I have going on right now.

Why wouldn't it be ok?

IIRC some have had 2000.

870 games, looks like they're 3 days per move.

Does it take you an hour or two every day to get through them?

If you spend 10 seconds for each game I'm thinking it takes you a little less than an hour each day.

There's no hard limit, but it depends for each person. I used ot run several dozen at once, and I came to resent the time I had to dedicate to them and began playing them mindlessly, timing out, and overall orchestrating the rapid destruction of my interest in chess. The right number varies from person to person, but at the risk of projecting, I think many people greatly overextend themselves.

I can't move in them all every day. The 24 hour games need one per day, and some of my other games will be below 24 hours by then too. With distractions, it takes maybe 2 hours.

I've found for myself that around 10 games with a 1 day per move works out great. Find your own bliss...

Yes, I calculated for you to simply not lose on time. So if they were all 3 days per move you'd only move in 1/3 of them each day. With that I came up with a little under an hour for 10 seconds per game. But including the time it takes to load the next game and orient yourself, that's probably too quick, and in any case that's a very difficult pace to keep up for even 10 minutes. I'm not surprised you say 2 hours.

A friend once played a guy here that had over 1700 games going at once.  I dont see how anyone expects to improve doing that.

Most games aren't terribly difficult to find a move in. Those might take just 10 seconds. Some of them require a bit more thought. I also have a lot of time on my hands, so that helps. Once the 24-hour games are under control, I usually move to the 7- or 14-day ones so that my opponents don't have to wait as long. Thankfully, those tournaments are usually explicitly called "SLOW CHESS" or something, so the disclaimer is taken care of.