First read your contract sometimes they would trick you to sign anything anywhere and will you know when this it's too late get the mechanic info get evidence of inappropriate work take ur inspection report 2 the dealer if not agree 2 fix then take the dealer 2 cort.

My state doesn't even do vehicle inspections, anymore. Hasn't done so in many years. If inspection places don't drive the vehicle and no check engine lite on and no codes. I don't know if they do sniffer tests? I thought inspections was mainly for emission issues? I guess you filled it up with oil? Your talking about engine oil? You didn't check anything on this vehicle before you bought it?
After reading your post, that whole vehicle has got me worried, not just the sticker. Take it to different mechanic have him give it the once over. See if it is safe to drive. I can't see anything from here. Safety is your responsibility.
I can't comment on the dealership. I don't know. I don't line in New York state, I don't know the laws?