I have always found that a really good favour you can do both your dog and your bank account -is learn how to trim the nails yourself. Get the right clippers, and teach him to stay still for you (or get someone to hold him still) Make sure the light shins through the nail so you can clearly see the delineation between the "quick" and the dead nail at the end. And never trim TOO close to the quick.
But it's true that the more frequently the nails are trimmed close to the quick (without being so close it could become a problem) -the more the quick will gradually recede.
If you did this yourself, you could do it very often, and wouldn't be tied to vet appointments, groomer, etc.
Also if you are short of money it would help.
Hello. Cute little dog you have. Well, I'm not sure I am understand this right but seems he has problems with the leg/foot that was broken? I would think, the only you can determine what is going on for sure is take him to the Vet (possibly another one or an Ortho Vet if you have one in your area) and get an x-ray on that leg to see if they can see what's going on for sure. Other then that, no way to tell. I had a puppy break a leg years ago and had it casted but it stayed on!! As she matured, that let turned out a bit but she had no problems.
As to the nail issue, if I'm understanding that correctly, you might try trimming it weekly (do you have a Dremmel) and see if that quick won't recede. Other then that, if/when your dog goes in for a dental or something where anesthesia is needed and the dog is asleep, ask the Vet to cut that nail short. It will maybe be sore for a couple of days but at least the dog will be asleep when it is cut. You would then have to make sure you keep it trimmed every one to two weeks.