hairless mating with DSH - offspring?

Hi, my girlfriend and I were talking about this the other day. If you have a hairless cat, can it mate with a normal cat? And if so, would they half be hairless or a quarter be hairless? Or would it be recessive and they would all be haired and carry the hairless gene?

You bet they can!
The hairless gene is recessive, so a hairless cat has 2 copies and cannot pass on a gene for hair. The kitten hair coats will depend on the genotype of the haired parent. If it has no hairlessness in its pedigree, it's probably got 2 copies of the gene for hair. So all kittens will have one "hair" gene and one "no hair" gene and will have hair.
If the hairy parent is a carrier of the hairless recessive, however, then half the kittens will get the gene for hair, and half will get the gene for no hair. Match this up with the no hair gene from the hairless parent and you will get a litter that is 50% hairy and 50% hairless on average.
Note that the very first hairless kitten from such a mating tells you that the haired cat is a carrier. This is what we would call a "test mating" to detect carriers of this recessive gene.