No, you don't need to waste your time sanding between coats. As long as the new coat of paint is the same kind, it should bond well with whatever coat is below it.
Two coats of varnish are usually enough for an acrylic painting. Be sure to apply the varnish in thin coats, and wait for each coat to dry before applying another.
You're sitting in it! Even if you're just driving for a few minutes, you've got to take the fur coat off. Fur is very unforgiving when it comes to friction...
You would likely need a large or XL depending on the brand's cut, etc. I would suggest trying the clothes on or ordering from a provider who allows free returns.