Orbits are circles or ovals, and the satellite must always be moving to stay in orbit. But the time to go around depends on the distance, so there is a distance where the satellite takes 24 hours to go around, which matches the Earth's rotation, which is geosynchronous. A subset of these is called geostationary, when the orbit is a circle around the equator, so it stays in the same spot of the sky. (Then we can aim a ground antenna just once and don't have to adjust it.) Satellites at this distance add 1/4 second delay to any signal because of light speed. This orbit is very tight, since it can not vary in altitude by more than a few hundred meters. (More than that would cause them to drift east or west out of the assigned spot.) There are a limited number of "slots" in this orbit to keep the satellites safely separated and to prevent their signals from overlapping. Most of these are used for communication, especially TV. A few are for weather, as they can watch an entire hemisphere constantly.

Other satellites operate in a lower orbit. Here the orbital period can be as low as 90 minutes. Most of these orbits are inclined so they pass over most of the earth instead of just the equator. The orbit (circle) stays in one angle while the earth rotates underneath. Satellites here get better images because they are closer to Earth, but take a day (or more) to see everything. They also have greatly reduced light speed delays. These orbits eventually decay because of tiny amounts of air at that altitude.

Yeah there are many, but the two you will hear about the most are LEO and GSO.

LEO is Low Earth Orbit, and is basically right at the edge of space. This is close enough that they can bounce signals around the Earth quickly, but far enough that there is not a lot of atmosphere. These tend to fall out of space pretty easily unless they have some onboard boosters to adjust their orbit, as otherwise the thin air does eventually slow them down.

GSO is Geo-Synchronous Orbit, and is far enough away that the orbital period is perfectly matched to the earth's rotation. That can be useful for all sorts of reasons, such as maintaining continuous contact above a fixed point on the equator.

If you want a nice fun dive into orbits and how they work, I suggest you follow Scott Manley. He has some very wonderful educational videos on the subject.

https://www.youtube.com/watch?v=i5XPFjqPLik

Others have mentioned geosynchronous satellites as examples that can just sit in one place, but they can only do so over the equator—not directly over North America as per your question. (They would still be visible from North America, bu they would appear to the south instead of directly overhead.) Geosynchronous orbits can be inclined relative to the earth’s axis, in which case they could pass directly over North America; but they would have to spend an equal amount of time over the southern hemisphere (without moving significantly east or west).

Yes and yes

Yes, all of that. They move in all kinds of directions and at differend speeds and heights. Some are fixed in a https://en.wikipedia.org/wiki/Geosynchronous_orbit

Satellites are spaced in height so they don't collide.

Most move somewhat towards east and not in the other direction because rockets use earth's rotation as a speed boost if they can. But there are exceptions to all of that and I'm not an expert.

What I know is there are lots of use-cases. A communications satellite probably wants to be fixed in a geostationary orbit so it stays reachable and you can watch TV all day without moving the dish. Or a satellite needs a low orbit so the latency or your internet or phone connection is low. A weather satellite may use an orbit that is in sync with the sun so it takes pictures everywhere at a fixed time of the day... Other measurements can be done better if a satellite has a high speed compared to the ground it is observing...

My buddy does orbital mechanics or whatever for Amazon currently, he explained to me that satellites have tracks which are paths at different elevations and directions to ensure they don't hit each other. One time he fucked up and the company's satellite entered another's track. He was beside himself thinking he was going to be responsible for the destruction of multimillion dollar satellites. Luckily they never hit and life went on.