I'll give this a shot,
There are 4 values you need to pay attention to here.
Satellite Position This is the actual position in the sky. Geosynchronous satellites are located directly above the equator. The satellite position is the place along the equator the satellite is located ( a satellite located at 90w would be located directly above the intersection of the equator and 90 degree west longitude.)
Azimuth is the satellites compass direction relative to your location. If you were in the middle of the US on the 90 deg longitude the sat would be straight south (180 deg). On the east coast the value would be larger, on the west coast it would be smaller.
Elevation is the satellites height above the horizon relative to your position. If you were on the equator the elevation would be 90 deg, the farther north you are the lower the satellite would appear.
Skew This is where I need a diagram. Because we aren't on the equator the line of possible sat positions describes an arc across the southern sky. In the middle of the US the highest point of that arc is about 50 deg elevation. The skew setting is adjusted to keep the dish aligned with the satellite either vertically or horizontally as the position on the arc changes.
Ok to some of your questions,
The elevation you mentioned shouldn't be a range like between 10-35 degs, it is usually a specific number, usually down to a tenth of a degree. The dish has an elevation adjustment on the mount, make sure the mounting mast is plumb and set the adjustment to the correct number. As for your hill, get a compass and get a line on the direction the dish needs to point. Then get some kind of angle finder, point it in that direction, and if you see clear sky your golden. Technically you only need a clear spot in the sky that is as large as the dish itself, as a practical matter you will want to allow at least 5 deg in all directions.
The skew numbers you gave are actually about the same. The sat finder program gave you 67 deg which is 67 deg above the horizon. The satellite dishes scale zeros out at 90 deg vertical and goes either left or right (+21 deg or - 21 deg for example) So the 2 numbers you got are actually within 2-3 degrees of each other.
There can be more than one satellite near enough to each other that they would share the same "location" as far as the numbers are concerned. If they aren't using the same frequencies they won't interfere with each other.
Your hillside can't be 106 degrees. If it was 90 degrees it would be straight up. At 106 degrees a big portion of the hill is hanging over you, I would move immediately and not worry about getting your internet going.
Ok now for the kicker. DBS (tv) dishes aren't that difficult to point with a little fore thought and some patience. 2-way satellite dishes are a a different animal. You don't just have to get a signal, you have to point the dish at the satellite well enough so that the return signal doesn't interfere with the satellites operation or they won't even turn the thing on. It is just not something they let anybody do. You will need to find a certified Starband installer or a way to fake it even if you do get the thing pointed right.
The way things seem to me you would be better off spending your time trying to find an installer rather than trying to do it yourself. Even if you could find an installer that is experienced with Hughsnet (used to be DirecWay) you would be better off. You made no mention of what part of the country your from but I bet there is somebody around.
with me to tell me how I can pre-check this site and know exactly where the dish will work. 
