INSURANCE, REGISTRATION, INSPECTION
INSURANCE- In New York State, your liability insurance from your car automatically applies to any trailers you tow. However, if you want physical damage coverage (aka comprehensive & collision) you'll need to purchase that coverage from either your auto insurance company or your boat insurance company.
REGISTRATION- Trailer registrations are renewed annually. Every year, NYS DMV will mail you the renewal bill. Once you pay it, they'll send you the renewal registration along with the new sticker for the license plate. Just like motorcycles, the sticker color changes every year.
INSPECTION- You have wrong information. ALL TRAILERS MUST BE INSPECTED ANNUALLY. The inspection sticker number might not be needed to submit the registration papers, but without it you will be fined. All inspection stations are authorized to inspect trailers. The cost is only $10 a year. Look at this DMV website and you'll see that it also confirms that trailer inspections are required...
http://www.nydmv.state.ny.us/vehsafe.htm