Every State is different and in New York each County is different. The fast easy way to find out is call a local gun dealer. A more through way is call the State Attorney Office in your county and ask them.
Yes you can. Just go to a gun shop, fill out the paperwork, wait for the background check and it's yours.....after you pay for it of course and providing you pass the background check. if you live in NYC it may be a whole different game and i think there might be some other cities that have their own rules too. Albany has/had some of their own rules regarding some long guns unless it's changed. It may have been "assault rifle" registration which is the whole state now anyway.