Breeding animals is a well-paid off business. Breeders get paid by commision, and in most cases commision is alot. Breeders usually specilize in one or two species of animals, and the price of breeding depends on the animal's average litter size, and/or the rarity and quality of the animal itself.
But enough of that, on to how breeding actually works.
Obviously breeding should be kept to the animals own species, but there are always a few minor exceptions. Dogs can be bred with wolves, horses can be bred with donkeys, sub-species can be bred with different sub-species. But other than the obvious, no, different species cannot breed.
Secondly, a female who is expecting cannot be put to work, or to show. They must be looked after! No one wants to see a litter full of stillborns. Once the litter is born, the mother is still going to have to be kept out of activities until her offspring are alright to fend for themselves. By then the owner of the mother gets to choose what he/she/it will do with the litter. They can sell it, giving a percentage of the profits to the breeder, they can keep it, and pay the breeder full-out, or they could give it away to friends, family, random people on the streets, and pay the breeder full-out. Really, the possibilites are endless(but they'll still have to pay the breeder, or come to an agreement). If, of course, the owner of the litter chooses to give one of the youngling to the breeder, and the breeder will take that instead of money, the breeder gets first pick of the litter.