For the safety certificate, they have a list floating around somewhere on the web and it's super extensive what they check. They gave us a list of things after the inspection that it needed to pass and give us the certificate. Some stuff was valid, like sure, brake pads, ok...but we needed to get a whole set of tires too even though we had only got them changed 1.5 years ago. It was also 3 hrs of labour for all the stuff so that was $$ too.
For the license thing, I hope it goes better for you. New York state just has a poor driving abstract though and other states are probably better. My husband also had a license in Washington state before and the driver's abstract was fine and showed date of issue. They wouldn't accept it though for driving experience because he had exchanged a WA license for his current NY one (even though they told us to get that abstract!) Basically just don't live in NY and you'll be fine
Good luck!!