Will you be out of state when your inspection expires?
yes
You can apply for an extension. You should also find out if an expired out-of-state inspection is a violation of law in the state you will be in.
what day of the month will my inspection expire?
The inspection will expire the last day of the month punched on the inspection sticker
do you have a list of what will be checked during the inspection?
You can look at the DMV brochure, New York State Vehicle Safety/Emissions Inspection Program for Cars and Light Trucks, it  lists the equipment items checked during a safety inspection.
can you also tell me what to do when an inspection sticker comes off?
You can reattach it to the windshield with clear tape or a small amount of clear adhesive.
what if the sticker is all messed up?