Not the roof itself, but its exposure. A cottage that used to sit low behind its neighbors now stands clear of them, and the wind off Jamaica Bay reaches it directly. Edges and corners are where that shows first, so that is where an inspection here starts.

It is common on an island four blocks wide with salt in the air every day. The roof covering can still look fine while the metal holding it down is going. Rust at the nails and the gutter joints is worth looking at rather than waiting for a leak to make the point.

There isn't one. This is New York City, so the New York City Department of Buildings is in charge, not a village board or a town building office. Small repairs that don't touch the boards or frame underneath don't need a permit. Once a job reaches that part, a permit is required before starting.

Your lot is private land sitting inside the Jamaica Bay Wildlife Refuge boundary, and the roof over it is a city Buildings Department matter like any other. Where it gets more involved is anything reaching the shoreline or the water, which brings other agencies in. Ask before assuming either way.

That is a question for your insurer, but the two usually sit apart. Flood coverage is written for water arriving from outside and below, while wind and rain damage to a roof normally falls under the homeowner's policy. Photograph what you can see before anything gets moved or cleaned up.