I moved your post because I think it deserves its own thread.
Taking your questions in order. . .
Marine Ich isn't too difficult to identify. However, not every white spot is Marine Ich (Cryptocaryon irritans). If you can post a closeup photo where the fish fills the picture frame, we may be able to better see what it is you're looking at.
The 'white gunk' could be mucous coating coming off the fish. Anemonefish have a particularly thick and abundant mucous coating. They shed this coating in times of stress (water quality, environment, poor nutrition, etc.), illness, and disease.
The black spots could be symptomatic of another kind of condition that is commonly referred to as Black Ich. A photo would help us help you and the fish best.
This is a photo of a fish with Black Ich: DisPic Summary
Unless I truly understand how and know the procedure of your LFS quarantine process, I will have to say I doubt they do a proper quarantine. Have you read these two yet? One is a good article, another is a step by step procedure for a proper quarantine process:
An Ounce of Prevention is Worth a Pound of Cure: A Quarantine Tank for Everything by Steven Pro - Reefkeeping.com
A Fish Quarantine Process. If your LFS is following this procedure, then I'd say the fish were properly quarantined.
Put another way. . .IF the LFS was doing a proper quarantine job, then your fish really isn't sick, is it?
A water change of any size should not be stressful to the fish IF it is done properly. Here are some good recommendations for a proper water change: http://www.reefland.com/forum/saltwa...tml#post159585
The value of a small but more frequent water change is keeping the water quality fairly constant. A large less frequent water change will help remove large build-up of wastes and nutrients. Either is okay. But if the water is of questionable quality, a large water change is a must.
You may be interested in learning more about water quality that the test kits you use don't show: What is Water Quality
Ask if you have other questions. Post a photo or two or three of your fish, if you can. However, I hope you'll do a lot of reading to delve into matters.