OK, the easy answer first. The butt scooting is usually the result of anal sac problems. The other possibility is tapeworms, which, considering the fact that she's a rescue, she probably has.
Now, to address the coat and skin issues. The cause is probably a combination of factors, again taking into account that she's a rescue. Diet is almost certainly one factor. A heavy load of intestinal parasites (tapeworm, round worm, hook worm, and/or whip worm) is another. The heartworms are also a factor, as well as the treatment for them. If she had fleas, that's also a factor. One other possibility that needs to be ruled out is the skin mite Cheyletiella Parasitavorax. This mite causes a condition called walking dandruff, and it's becoming more common. It's also easy to get rid of, so don't panic.
I'm sure your vet will sort this all out for you, and in time her skin and coat will recover. It does take time, though. Get her on a good diet, take care of any parasite problems, give her a bath in a high quality shampoo, or have her professionally groomed, and wait. In a few months her coat and skin should look 100% better.
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