Well...hmmm...
Let's put things in perspective here: When you bought the car, it looked... ghastly. Given that, I think you've already made major improvements! I can see that you've spent some serious elbow grease in sanding to get the orange peel out, also well done. As for spots of the original paint coming through, I'll say two things. 1- it looks like some of these spots are either along edges or creases in the panels. 2-The others look like they are at areas that are dented (?). You have to be VERY careful when sanding edges/creases, especially if you're using a block. I think you've just over sanded in those areas. BUT...
You've also only got three coats on, correct? If you're laying the paint down properly, you wont completely cover the underlaying paint until the 4th coat. And that's assuming that you've layed down 4 nice coats. You've put on three, but judging on how much you're sanded to get all the orange peel out from the first two bad coats, you're really at more like 1.5 coats.

All in all, I think you're making major improvements. I know it doesn't feel like it, but you are. NOW... do yourself a HUGE favor... FORGET ABOUT THE SPRAY GUN!!! At least for now. Unless you've sprayed a car before, you're just BEGGING for more trouble. Slow down, get out a fresh clean NEW roller, and just concentrate on one panel. The hood is a good place to start. You've already learned quite a bit (I think), I'm willing to bet that the next coat will go on much better; as long as you don't get impatient.

As for the $100 - consider the alternative. Getting anyone else to paint your car, even the CHEAPEST, sloppiest spray job would have cost you 4 times that amount, and guarenteed you would not have been happy with it.

Next time you're out, take a good look at the paint jobs on cars, even new cars. You'll find that virtually all of them, except for the very high end cars, have a certain amount of "orange peel" to the paint. And the darker the color, the more pronounced it will appear. You "could" get rid of it entirely, but it is a very labor intensive job, even with a perfect spray job.
By keeping that paint thin, the amount of orange peel you will get is minimal. I think you just had a bad case of it because your first coat was way too thick. Go back and look at the first photos you posted.