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Originally Posted by MarkCK
1) Where do I place the sun on the artificial horizon.

For celestial bodies that have visible discs, the Almanac lists coordinates for the center of the disc. However, it's hard to line up the center of the sun with the horizon when you do a real sight; much easier to line up with the lower limb (edge) and then add half the sun's apparent diameter (listed in the almanac).
When using an artificial horizon, there is no horizon and you line up the sun with its reflection exactly. So the centers of the images lines up and you can use the Alamanac values directly, except...
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2) Once you have your angle from the artificial horizon do I divide it by 2 to get the angle that I use for my calculation?

Almost. You never assume you sextant is perfectly accurate; after you have removed as much error as you can, there might be some left. This remaining error is called "index error", and you need to measure it before you can use your sights. To do this you usually sight the horizon, or another distant object, and line it up with itself. Then read what the sextant says: that's the index error. This value must be subtracted from the sextant reading before any other operations are performed.
E.g. if you check the horizon against itself and it says +5' (i.e. "on the arc"), then you have to subtract 5' from your sights. "If it's on, take it off".
The index error is an error "in the sextant", so it's the first correction you make.
For artificial horizon sights, you then have to divide by 2,
after taking off the index error.
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3) I am having a little trouble figuring out what my exact angle is with this sextant. I think I can figure out degrees easy enough. But what about minutes on the vernier.

I won't give a detailed explanation of vernier scales here; yours is thankfully straightforward (I have a calipers with a vernier scale indicating 128ths of an inch... a bit more confusing).
So, the 0 mark on the vernier gives you the number of degrees. Remember to look to the right of the zero to get the number, if the zero falls between two ticks on the arc. Then, to get minutes, you find the tick on the vernier scale that exactly lines up with a tick on the arc; the label on the vernier scale gives the number of minutes.
I'd put those measurements as
1) blurry, can't read
2) 64°00'
3) 83°00'
4) 26°12'
5) 52°58'
One thing that I find helps with vernier scales is to look "past" the tick you think is the right one, in both directions. For me, it's easier to see the ticks "diverge" from the most exact one, and then you can sort of follow it back to the "center" or "least diverged". Often you'll find that two ticks on the vernier scale are "inside" two ticks on the arc; when you see that, your answer is halfway between the vernier ticks.