It's true, there is a potential for missing keystrokes. In practice this rarely becomes a problem, because humans just aren't fast enough to beat the update loop. At very low update rates you will be missing keystrokes though.
In my experience it starts to get dangerous once you get below 20 updates per second. A quick search on human keypress timings also confirms that number. The average keydown time seems to be around 100 ms, where 50 ms seems to be the lower end.
To give you an idea what those update rates mean for video games. The target framerate (at least on PC) is usually 60+ fps. 30 fps is usually considered the minimum. At 20 or less fps most people would probably consider a game as unplayable. Of course it also depends on the type of game.
While not being a big problem in practice, I think there is a bit of a weakness here. Having an event-based alternative to the polling system would be nice. MonoGame does have an event-based alternative for keyboard input, but that seems to be mostly geared towards text input.
Not really, the most common scenario is to have one update for every draw.
Yes, Windows uses an event-based input system under the hood.