It sounds like most of the stuff you've listed is at least partly right. Drink lots of water. Get lots of sleep.
Things like vitamin C and zinc will help keep your immune system functioning properly if you consume them in sufficient quantities on a regular basis, but they won't really cause you to "get better" right away if you're already sick. I seem to remember hearing that someone was bringing a lawsuit against Airborne for false advertising, but I don't remember the details of the case...
It IS a good idea to stay away from milk if you're having issues with mucus, but milk doesn't actually cause your body to increase its mucus production - it's just that some of the stickiness from the milk itself stays in your throat when you drink it, which, if you're already dealing with sticky nastiness there in your throat, just exacerbates the existing problem.
I'm not sure what the deal is with chicken soup. If I had to make a guess, I'd say that it's a good way to consume good things like protein and veggies in a form that won't irritate your throat quite as much when you swallow it. Plus, heat and salty liquids are a VERY good way to soothe a sore/scratchy throat.
For example if your throat starts to develop white dots, it could be something more serious like bacterial strep-throat, which means you should go to a doctor to get some antibiotics to remove it quickly starting as soon as you suspect it (they can do a swab culture to verify if that's the case).
Tombb is right, especially about this part. If you shine a flashlight into your mouth while looking in a mirror, and you see white dots on your tonsils, it's usually a good idea go get a strep test. Strep isn't the only thing that causes white dots (which are really pus) on your tonsils, but most of the other things that cause that aren't good either, and strep can cause other, more serious, illnesses if it goes untreated.
EDIT - Whoops, wrote that while you were posting, Alec.