2) They all orbit in the same direction.
3) There are a number of different orbits, but they are all inclined at the same angle.
The illustration on that page was, I'm afraid, drawn by someone with no clue what the constellation actually looks like.
2) They all have polar orbits that reach the same location 4 minutes earlyer each day. However, there horizontal ground speed relative to a stationary observer changes over the course of their orbit. (It's zero at the pole and maxes out at the equator.) And is also diffrent form the other satilites you are comparing it with.
Which is why you get those S shaped paths: http://www.n2yo.com/satellites/?c=20
3)I agree but see 2.
PS: Yea, that picture was fairly bad, I was looking for an easy to read article not a picture. The classic picture of a constilation with fixed polar obits is vary misleading once you take the earth's rotation into consideration. It's rare to find something that shows both the orbit's and their horisontal velocity fairly accuratly without making it look like they interweave. I once saw an animation showing the orbit of 4 satilites and the area they could cover area just those 4 satilites could give you coverage of but it's far harder with just a picture.
None of the satellites are in a polar orbit. The orbits are inclined at 55° to the equatorial plane.
Now suppose P1, P2, P3 velocity is more than 2x that of point U and you have you have new offsets from U to {P1,P2,P3} you are now going to have a new curve (c2) in 3d space, but you know U's vector must take it from c1 to c2.
Now add another time cycle, and you know it's vector must take it from C1 to C2 to C3. As you keep adding C's you constrain both the valid vectors(direction and velocity) as well as positions.
Now measurement accuracy as well as change in velocity limit the accuracy but GPS satellites are moving a lot faster than you are so you can get reasonably accurate information this way. Edit: Also you can basically ignore the sections of the curve that whose altitude is unreasonable so the solution space is fairly constrained to start with and for each subsequent curve. But you can also use an internal clock/oscillator, accelerometer, gyroscope to further constrain reasonable accelerations etc.
I agree on the other points. They all have an inclination of 55° in regard to the equator. See Wikipedia [1] for details and a more serious illustration
You would need three if you had an atomic clock: if you knew the precise time. But in practice you do not. You have a good clock that has an unknown shift with respect to the clocks in the satellites.
So you can measure differences in times, but not absolute times. I.e. you do not know the distance from the gps to the satellites, you know the difference of these distances. So you need a fourth satellite.
This was designed because it is easy to make accurate relative time measurements, but hard to have an absolute time reference.
Don’t forget we have a lot more CPU to throw at these problems than they did in 1980.