When it comes to daily games, the amount of games that you choose to run at once depends on how many times a day you are on chess.com and how you want to utilize this game mode. If you are on once every couple of days, then your time control should be a game every 3-5 days.
In regards to how many games you want to run at once, that depends on whether you are using daily games as a form of rapid chess (You play a large number of games and thus can devote that much time to each game), or as a form of classical chess (You play fewer games so you can focus more of your time to complete each move). When I played I wanted to be able to take my time with each move so I only ran 6-12 games at once on a move every 3 days time control.
You can always start small with 4 -6 games and then start more games if you feel that you can handle more.
I'm pretty sure that you can set up e-mail and/or app notifications when your opponent makes a move so that you don't need to check in periodically to check the status of the games. So the choice of making moves in your games as they happen at once or making them all at once doesn't matter and is up to you.
I'm posting this link so that you can see what is and isn't allowed in daily games. I suggest that you read the rules to see what is and isn't allowed so that you utilize all the available resources that you have at your disposal.
https://support.chess.com/en/articles/8583921-what-counts-as-cheating-on-chess-com
I'm just now tipping my toe in the water with Daily games and just looking for some general advice.
How many games would you recommend to have running at once?
Should I check in periodically to see if my opponent has moved or is it better to set aside a particular time of day to check-in and then make all of my moves in one session so to speak?