There will be no record of an inspection on New York State DMV records. You cannot renew the registration if there is no DMV record of an inspection within the past 12 months. If you must renew the registration before you get a New York State inspection, call 518-486-9786.
You will need to blanch a piece of cabbage or lettuce and then sink it in your tank overnight. The next morning you can just pick off the snails from the piece of cabbage and repeat the process with fresh lettuce till the numbers come down. This methods is effective against all snails but not against snail eggs.
You can add all sorts of pond plants to a turtle's tank or pond and find out what they do and do not eat. Turtles that are inclined to eat plants will eat most floating plants like duckweed, azolla, frog-bit, water hyacinth, and water lettuce. Most submerged plants are also eaten like anacharis. It is said that most turtles will not eat cabomba. Lily leaves are relished so do not put expensive ones in with turtles.