About the pistols. He cannot bring them into the state without a NY pistol permit issued by the county he resides in. He cannot leave them with a FFL until he gets his pistol permit because that means he will have them in his possession without a permit prior to surrender, which is illegal and obliges the FFL to inform the police. He may be able to find an FFL that will accept them if they are shipped directly to the FFL from out-of-state, pending a permit, but he cannot just bring them to the FFL himself. It puts the FFL in a tight spot. Once your son acquires a pistol permit, he can legally have the pistols transferred to his local FFL, who can then transfer their possession to your son once he registers the pistols on his permit. If he has high capacity magazines that hold 10+ rounds, he must be sure they are pre-ban magazines. He should double check this with the FFL as well when he has the pistols shipped to the FFL - many of them will not release a pistol with high capacity magazines that were transferred into the state. The magazines will be destroyed, and the FFL will likely offer to sell him compatible NYS compliant magazines. If he knows the magazines are pre-ban (even better, if he can prove it) he should have the magazines sent to him directly and separately from the pistols, and they should not go through the FFL.
The requirements for acquiring a pistol permit vary from county to county depending on what the county judge requires. Some require a handgun safety course, some require a NRA handgun course that includes live fire, some may have additional or other requirements as well. Many judges will not accept other courses other than the one they require, and will not make an exception - currently the waiting period just for the required course in my county is over 9 months. A friend of mine who is a NRA Firearms Trainer in several different disciplines moved to my county and had to take the county course to get his NYS permit; the judge would not provide him with a wavier despite a career in firearms handling. Residency requirements will vary from county to county. Most require a number of references from other people that live in the same county, and that you have known for a minimum of 6 months to a year. Some judges will waive this requirement and accept references from out-of-state if you write a letter to the judge, others will not waive this requirement.
My best advice is for your son to contact the Sheriff's department and/or the judge in the county he will be residing in to start the application process now, and to find out if he can get any exceptions or waiviers for things like the reference requirements. I've lived in NYS all of my life, have never been arrested, and still spent over 9 months and several hundred dollars to acquire my (hunting and target) restricted pistol permit. Unrestricted isn't even a realistic option in my county.
Good luck. I'm sorry to be so negative in this post, but NY does not have an efficient, consistent, streamlined, or even logical pistol permit process.