I think the answer is in your question. It's about balance IMHO. Directed effort. Not too many games. Some study. The study being directed towards the areas of the game. Study the endgame - it's like eating your greens.
How much chess should you play to improve?
I've heard it said to study every single loss, spending a lot of time doing so. I'm thinking there has to be a balance, play a few until you get a good loss to study. Study that loss, rinse and repeat. I suppose if you learn why you lost each one and never repeated that mistake, it would systematically take away your weaknesses one by one. I'm thinking that is what I will try to do. Good luck!
When I use to play online I'd start playing standard games 35-60 minutes (no blitz) at 4:00 PM then stop around 2:50 AM the next day rest go over the games and then crack the books and study for 3 hours the next day when I was rested come back and play some more.
I also played alot of CC games 150-200 correspondence games at a time.
You asked what are some signs you should stop playing...............
You're creativity isn't there you lose to people you normally squish like a bug and are making simple mistakes, fatigue are you feeling wired when you played stressed? headaches? emotionally drained? all those are signs you need a break.
What are some indicators for when to stop playing? Is it better to only play a handful of games and analyse them or play as often as you can? What do you think is the right balance of play and study when you try to improve your chess?