Yes it is dominant; I know nothing about hairless genetics. You could try the search function of this forum. I know there are several members who could help with this. Your mousie is also long haired in addition to being rex (otherwise called Texel)? That's one very, very hairy little beastie!
You're misinformed on a few counts... Rex (Re/*) X Rex (Re/*) does not create hairless in mice or anything resembling hairless. It creates a version of hairless in rats, but the rex gene that rat people work with is slightly different from the Rex gene in mice. In mice a homozygous Rex is simply a Rex who has slightly tighter curl that lasts longer into adulthood.
Rex is completely dominant over standard coat but that does not mean all his babies will be rex. Here you're confusing complete dominance with homozygosity. If he is homozygous, all his babies will be Rex. This has nothing to do with the type of dominance of the allele that causes Rex fur, though.
Also, fuzzy (fz/fz), when homozygous and selectively bred over the course of many generations, can produce somewhat hairless mice (known as "fuzzy hairless"). You might be confusing Rex with fuzzy, but they are separate alleles of separate genes with different modes of inheritance (one is dominant, one is recessive).
There are a lot of mutations of coat in mice, so it's easy to get confused if you're new. Feel free to ask any further questions you have!
His mum had the same kind of curly coat with long guard hairs, but I'm not sure about his dad. If his dad wasn't carrying the rex gene, then he's heterozygous for rex, I guess. Will he therefore have a 50% chance of passing the coat on to his offspring (assuming he is put to does not carrying the rex gene)?
How about the longhaired aspect, assuming Moustress is correct and he is a Texel? I only have short haired self coloured does at present, so I'm wondering what he'll throw out. He looks just black and white in this pic, but he actually has a tan patch underneath.