All 50 states, drawn at random, with a no-repeats mode that turns the list into a shuffled deck for classroom games.
All fifty states are included and each is equally likely, which is the right behaviour for a quiz or a classroom game and worth stating because it is not how people guess. Asked to name a state at random, most people produce California, Texas, New York or Florida far more often than chance would. The large and heavily featured ones crowd out the rest. A uniform draw is precisely what corrects for that, which is why it makes a better teaching tool than asking a room to shout one out.
With no-repeats on, the draw behaves like dealing from a shuffled deck of fifty: every state appears at most once, so a quiz can run for fifty rounds without duplication and a classroom activity can assign each student a different state without collisions. That is the mode most teaching uses want. Switching it off gives independent draws, which is right for a warm-up where a repeat does not matter and each pick should be a genuine coin-flip rather than a card removed from the deck.
Yes, the full list, each equally likely. Territories and the District of Columbia are not included.
Yes. Turn on no repeats and set the count to 50, the draw then behaves like dealing from a shuffled deck.
No. Wyoming is as likely as California, which is the point. It corrects for the bias people show when picking a state themselves.