You're starting to see the results of the improved diet! I use regular fine combs on my cats, the little black ones they (used to?) give kids on picture day at school.
However one of my cats did steal my boar bristle hair brush, she loves me using that one her. I think the comb takes out more fur, but the brush is a bed time treat.
They each have their own routine for combing. You'll have to figure out what works for him. He'll let you know.
Here's my method for nail trim training:
How to train a cat to accept nail trimming. My Method. (it works!)
Get kitty used to having his/her paws touched. You can do this any time kitty is relaxed, stroke the paws, hold them between your fingers and apply pressure, when the claws extend, stroke in between the claws and so forth. But you also want to make the training more purposeful. I call that Paw Work.
Use treats for incentive. Something wet and smearable is best. Depending on kitty's preference, softened butter, yogurt, even cream cheese can be used. You don't need to use a lot, just make sure it's soft enough to smear. You can place a tiny dot (less than pea sized) on the mouth, and kitty will be licking it off as you work.
Decide on a position you intend to use for nail trimming, whatever is most comfortable for both you and your cat. I sit on the floor and hold the cat in my lap (upright). I used to have the one kitty perched on the table, draped over my arm, because I thought that's what she preferred, but lately I've found she prefers being held in my lap on the floor, like the other cats.
**Paw Work** (do daily during training)
Get treats ready.
Get kitty into position. Tell him/her what you are doing and why. Speak in a soft voice, use kitty's name a lot, offering many reassurances, throughout the process. Be confident.
Place a tiny blob of butter (or other soft wet treat) on kitty's mouth and while kitty is working on treat, take each paw and hold it between your fingers and thumb and gently press to extend the claws. Use this time to look carefully at the claws. Notice where the quick is, the pink part, you want to avoid snipping close to that, as it will hurt and bleed.
After each paw, give a treat (another lick of butter, or whatever). Then release kitty and give one more treat.
If kitty struggles at first, be firm and hold on. Speak softly and reassuringly. Kitty needs to learn that struggling will not get him/her released, and that what you are doing is not going to hurt in any way.
Of course, use your own judgment about if s/he is getting TOO upset. You don't want the cat to get traumatized, but you don't want to give in too easily either. If you do release kitty, give a 15 minute break, then resume, until all paws are done.
When you think kitty is ready, instead of just looking at the claws, snip the tips. I suggest just starting with the tips until you gain skill, to avoid getting the quick. As you become more practiced you will be able to cut them a bit shorter.
If you can only get one tip in a session, that's fine. Slow and easy does it is the the way to success. Next time you might get two tips. And so on.
As you snip, continue to smear little dots of butter (or other treat) on the mouth as needed to keep kitty occupied.
When it's all over, give a final taste of the butter (or other) by offering it on a spoon or your finger, for kitty to lick off, instead of smearing it on kitty's mouth. (this is important, so s/he knows that's the end of it for that time)
PS Just remember there is no rush for kitty to learn to accept this. It takes as long as it takes. One of my cats goes berserk if her paws are touched. It took over three years of daily Paw Work before she would allow even one snip of a claw tip.
It took another three years to get to the back feet. She is now 10 years old and I can do all four paws in less than 2 minutes! She hates it and growls warnings through out but with her little smears of butter on her mouth she's too busy licking to bite or struggle. She trusts me and knows, even though she hates it, that I would never hurt her.
If you could hear her, making yummy noises and trying to sound fierce with her growling at the same time! GRRRRRyumyumyummyRRRRI'MWARNINGYOUmmmmumyummyRRRRR
I no longer do the daily Paw Work with her, but I did continue it for a long time.