No, all satellites do not orbit Earth at the same altitude. An good overview of this can be found on http://www.idirect.net/Company/Satellite-Basics/How-Satellite-Works.aspx. This overview reviews Low Earth Orbit, Medium Earth Orbit and Geostationary Orbits.
A "tilt" as compared to what?
No matter; the answer is "yes". Satellites are launched into orbits that are designed to facilitate the purpose of the satellite. So many reconnaissance satellites are in polar orbits, while TV and communications satellites are mostly over the equator. And depending on the purpose, at every angle in between.
Generally, no. If the altitude of the orbit is different, the speed of the orbit will also differ, and the two satellites will diverge.
About the only exception is for geosynchronous satellites, which all share roughly the same orbit a degree or two apart.
If it doesn't, then it's not an Earth satellite.
No. The satellites orbit in the Exosphere layer.
No.
Gravity
It has to do with the formation of the solar system. Since all of the matter that condensed into what makes the solar system bodies was spinning in the same direction while coming together, it would have taken a drastic event to cause one of the bodies to orbit in a different direction.
Some satellites cover the whole earth each pass, because that is what they are used for. However, many also cover nly certan regions such as the poles or the equator or one continent or one country. Geostationary orbiters for example, stay above the same place forever (that is, until they are taken or sent down by something). Many orbit over the same places each time, covering the same regions each pass. This is true of all satellites, the difference is how large the regions are nd how many of them. Some satellites cover the whole earth each pass, because that is what they are used for.
Obviously. Since they move in an ellipse around the Earth (or other central body), they change direction all the time. The only way NOT to change direction would be to move in a straight line; satellites don't do that.
Do all planets and satellites lie on the same gravitational layer?
All comets do not orbit the Sun in the same direction as the planets. Some comets orbit in a clockwise direction, while others orbit in a counterclockwise direction.
Yes, the satellites orbit in a geosynchronous orbit, as with most all communications satellites. (Some exceptions are satellites such as the global positioning satellites.)
No. That only applies to low Earth orbit. Geostationary satellites orbit beyond it.
no
Gravity
You would see the satellite in the same direction all the time. The satellite is supposed to move around the Earth at the same speed as Earth's rotation.
In fact, Venus, Uranus, and the "dwarf planet" Pluto orbit the Sun in the same direction as all the other planets. So all the planets orbit in the same way.However they rotate in the opposite direction to the other planets.
All of the planets in our solar system orbit the sun in the same direction.
All satellites pass the equator. Twice every orbit.
All satellites follow an elliptical orbit - they are darn close to circular, but even a circle is an ellipse.
With large number of low-earth-orbit satellites and the geo-synchronous orbit stuffed full of communications satellites, there aren't all THAT many "medium" altitude satellites. But there are some. The GPS navigation satellites, for example, are in highly inclined 12-hour orbits, and an unknown number of military "spy" satellites are in that middle range.
No - satellites do not go to the moon. Satellites orbit planets/moons/objects with gravity in space.