Need advice on whether to trap mom cat

Hello!
I need some advice... Yesterday I saw a stray or feral cat and kitten in the alley. I was trying to see if they were friendly and walked over, the mom stayed where she was but the kitten approached me but then got spooked. He ended up running across the alley into my yard, where my dog chased him (when I saw her and told her to "leave it" she stopped.) So to make a long story short, I caught the kitten but the mom is still out there. I left out food for her in the alley. The kitten is probably about 7-12 weeks old. The mom was very small and skinny, I'd guess she was still a teenager herself. I would like to trap the mom and try to find her a home as well or at the very least do a TNR with her (I've done TNR once before.)

The problem is I don't know if she might have other kittens somewhere. There are hawks and foxes around here and although the kittens are not at the nursing stage anymore they probably would not survive on their own...
I was thinking though, the mom was alone with the one kitten. I saw her late last night again, on my front lawn also alone (she ran because I was walking my dogs). I think maybe because she was young and small she may have either just had the one kitten or no others survived?
I guess my question is, should I assume there are no more kittens, and trap the mom? If not, does anyone have any advice for how to find any additional kittens there might be? The mom does not run immediately when she sees me but she is skittish.

If anyone is interested in seeing the kitten, here is a photo:

If the kittens are old enough to be weaned, I would do a TNR, personally

If you can trap momma, please do. It almost sounds like you might be able to "tame" her with regular feedings and some sweet talk. It also sounds like she needs a vet visit herself.

She might not be getting enough to eat after beging pregnant and nursing a kitten. If you do start feeding her, try giving her kitten chow, it has extra nutrients to make up for the ones used while pregnant and nursing.

Oh yes! The kitten is adorable. Have you named him yet?

I am calling the kitten Church right now but I might change the name. I'm not 100% sure he is male for one thing...

Here is another photo of the cutie. I think he's going to be a longhair?

Hey just wanted to give an update on the kitten.
He went to the vet today. The vet said he is at the most 6 weeks old. They can't vaccinate him yet since he is sick (sneezing, runny eyes.)
He is anemic and so they weren't able to draw enough blood, we have to go back in a week for the FelV/FIV testing.
He does have worms and they wormed him and gave him an antibiotic and vitamin shot, they also gave me a vitamin/iron supplement to give him at home to help get him stronger...hopefully we can test him in a week if he gets well enough...

I am worried because if there are any more kittens, they will not have a very good chance of survival since they are only 6 weeks old and winter is coming in fast (and they probably all are sick like this one). I haven't seen the mom in several days but I am leaving out food for her. I'm not sure how to find out if there are more kittens or not!

thank you for helping the kitten. Could you pm me what TNR means?