I had someone working on my car, but part way through, I realized he didn't know what he was doing and I could probably do a better job myself. Here's my situation:

He replaced the front quarter panel, sprayed it with primer, and then the base coat. He did a bad job with it, so he came back a couple weeks later to do another base coat. He did a better job, but while we were waiting for him to come back and clear coat it (he said the base coat had to dry for a week), some tree sap dripped on the paint and ruined a spot. I got the sap off, but now the paint there looks white instead of silver. Also, after putting on the base color and before putting on the clear, he glued an emblem back on.

So, I have a few questions:

1) It's been about three weeks since he last painted. If I clean and degrease the area, can I apply paint where it's needed and clearcoat on the whole panel, or do I need to sand it all first?

2) The paint right around the emblem is ok, but do I need to remove the emblem and clearcoat the whole quarter panel? If so, what's the best way to get it off without scratching the panel? When he took it off the old one, he used a screwdriver, with heavy damage to the old panel.

3) There is a part of the directions that sound a little unclear to me. How long should I wait between spraying base coat and clear coat? It says to wait until it's dry, but I'm unsure if that's a half hour, couple hours, a week?

4) The guy working on it before wanted to let the paint (metallic silver) dry a week, polish it, then apply clearcoat. I've read about painting in several places and haven't heard of anyone doing anything like that. Was the guy a moron who just had no clue, or was he possibly doing it right?

well, 97 views and no one responded, so i guess ill give my .02.  If he clearcoated over the sap spot you will need to wetsand with 600 grit to scratch up the clear and respray the base coat.  After you apply however many layers of basecoat you will need to wait at least an hour or 2, if it is hot (95+) i would wait until it got cooler out (right before dusk) to shoot the clear. 

If he did not shoot clear then you can shoot the area after you sand out all the blemishes, then put a light coat over the whole thing to get rid of any paint lines. 

I would take off the emblem, take a hair dryer or a heat gun and get the adhesive good and loose then try to pry it off with your fingers or a small screwdriver.  You can get adhesive to re-adhear it at Autozone. 

I dont know what that guy was saying about polishing the paint, you can wetsand it after it is dry enough with some 1000 grit paper and then use 1500 to get rid of the 1000 scratches before you shoot the clear.

You have to polish the clearcoat in order for it to shine.
However, a week is too long.
I would scuff the basecoat and wait till it dries (the reason we don't have an exact time is because it can really vary depending on the outside temperature. Sometimes, the basecoat  can dry in one hour, other times, it will need 24 hrs.).
I always recommend practicing off the vehicle first to get the feel for the paint, clearcoat, etc.
Hope this helps.