All public US equity exchanges are closed on the 9 US trading holidays (see below) and open on all other days. Exchanges also close early (13:00 ET) on the Friday after Thanksgiving and on the day before Independence Day if Independence Day is being observed on a Tuesday, Wednesday, Thursday, or Friday. (Some venues have extended trading hours as a matter of course; for them an "early close" might be later than 13:00 ET.)
To answer the second question, yes, if you know NASDAQ's or AMEX's holiday schedule, then you know NYSE's (modulo the timing of their early close). I'm not sure about the options exchanges; they're not regulated the same way and are a good example of exchanges with extended trading hours in the first place.
The US trading holidays are as follows. Note that trading holidays are not the same as federal or bank holidays, which include Columbus Day and Veterans Day but do not include Good Friday.
- New Year's Day
- Martin Luther King Jr Day
- Washington's Birthday (a.k.a. Presidents' Day)
- Good Friday
- Memorial Day
- Independence Day
- Labor Day
- Thanksgiving Day