I was also a beginner at the beginning of the year. I went out and bought Meguiars 105, and Meguiars 205, a chicago electric DA from harbor freight, and ordered orange and white hex logic pads from amazon. This will be a good start. Get these things, should cost between 120 and 150 for all of it depending on where you buy, and that DA goes on sale quite often, looks like it's currently down to 49.99, so now would be the time to buy. I started off doing my Formula and then did my Sierra, and now have had a few other people come to me for correction and have a pretty good grasp on what I'm doing.
This is correct but to expand,
I’d get meguiries M105 and M205 rubbing compound along with a porter cable dual action polisher
Amazon sells a good repair kit for that.
Paint correction is basically buffing your car's paint with a tool (usually) or by hand (rarely) to remove swirls, scratches, and small imperfections. Something good for them would probably be polishing compound, some good quality microfiber towels, or just detailing products in general really (there's a ton of different products).
I would say to get them some nice microfibers from The Rag Company and maybe some Meguiar's 105 and/or 205.
So, first of all, the toothpaste is old school. I would advise against doing that ever again.
Wet sanding is a common method used in detail but is not something just anyone should do. You also should have used a much higher grit sandpaper. Say 2000 or so. Your clear coat is not ruined nor do you need to re-apply it you just need a more effective method to restore it. Using a microfiber rag and some cleaner wax will not remove that dullness the sanding left behind.
You need to get something like Meguiar's M105 and use it on a machine with a pad. Much like your drill. After using a compound, you need to use M205 to follow up and remove any imperfections the compound left in your paint.
Wax will just cover it up, if you want to remove the scratch you need to rub it out with polish. I've had some success with Meguiar's M105 cutting compound + M205 swirl remover. Keep in mind, polish is actually an abrasive so don't go overboard. If you just rub it by hand you should be safe. Links: M105, M205, but any brand should work similar.
Unless you can bang out that from the back there's no hope to straighten it with home tools. It can be done from the outside with a stud welder + puller (video) but this is something best left to pros. It's much easier to replace the door for ~$200-500 at a junk yard, search car-part.com -- thats what my insurance did for a similar issue, came out to almost a thousand bucks at the body shop when you add the paint and labor on. But if you do it yourself you might be able to just get one in the right color and not paint it.
If you just want to fix the paint, just do the touch up. Call your dealer to get a small jar in the right color. You can fix the other less deep scratches with polish (heavy cut, light cut).
Also check this channel out if you are interested in how professionals do it: https://www.youtube.com/user/tussik01/videos
I was looking at this stuff but I have no idea if it'll work for this type of damage.