Litter size depends on the number of eggs released by the bitch and whether the mating takes place on the ideal day for the millions of sperm to meet the eggs at the right stage of ripeness for fertilisation. Whether or not all embryos implant depends on the bitch, who then might yet resorb.
In my opinion the size of a litter is determined by the number of eggs released by the bitch. Sperm are released in millions, so there's lots to spare there.
the sex is decided by y and x sperm just like humans. As for who decides on the amount of pups it does depend on how many eggs are released but if the male had a low sperm count then it is possible that all eggs would not be fertilised.