Cats fighting vs. playing? Let them fight or separate?

I recently introduced a new foster kitten, gray tabby, into my home about a week or so ago, who is 4 months old, clawed and not yet spayed (was too small to do so when the rescue found her) to my resident 10 month old orange tabby, neutered and declawed, who is a chunky and also playful kitty. I kept them separated for a few days, fed them on either side of the closed door, then opened the door with a baby gate separating them while they ate and there was no signs of aggression between the two. I've switched environments by letting the foster kitten wander the house and keeping the resident cat in a room as well. The foster kitten took a few days to warm up as she hid for the first day but eventually came out for snuggles and was very playful and energetic when I was working in the study (her safe room) just recently.

So I started to introduce the two, first by putting my resident cat under a laundry basket (didn't have a big crate) and letting the foster kitten wander, and vice versa, and they seemed to do great without any aggression still. The last few times I've let them play together supervised, or I play with them with toys. They chase each other, swat at each other, mostly without any noise. But then maybe 20 minutes later, the foster cat is hissing and yowling. Usually how this happens is the foster kitten lays on her back as my resident kitten comes after her and then there's fighting as they get all tangled up and a lot of yowling from her, and she has her ears back and claws out and my fat resident cat is pretty much sitting on her. My resident cat has not displayed any hissing, growling, ears back, etc. Also once the fight is over, not even a minute later they're back to playing again. Of note, nobody has been hurt. So after this happened a few times I just separated them. But now when I try to separate them, the foster cat doesn't want to go back to her room and wants to be let out and goes right back toward my resident cat. 

Everything I've read says not to let the cats fight it out, but there are a lot of stories and videos of people who have just let the cats work it out. I would love to eventually adopt this foster kitten and so them getting along or at least tolerating each other is important to me. It's only been about two days that this is happening. Should I just let them be and hope for the best or am I setting myself up for two cats that will eventually not like each other if they continue to fight? I just don't want to make things worse. Or should I repeat the introduction process, just slower and limit their playtime, and separate them before any fights begin? How much fighting should I tolerate? 

Thanks for any advice!

A further observation, the resident cat can be pretty rough, biting her everywhere, kicking her. I don't know if he's trying to mate with her? But my resident cat is a biter and has had issues with that since the beginning, so I know his biting hurts and the foster kitten is trying to let him know that but he is pretty persistent with her. The foster kitten is supposed to be spayed soon, per the rescue organization.