Some cats are spayed right on the delivery table if they had a caesarian section and the breeder doesn't want to use them again. I was surprized by this also as I thought it would interfere with milk production? Most vets say it's ok to do that.
A sign I look for in my cattery that the queen is going to deliver soon is that the belly ' drops.' It all of a sudden looks smaller and lower as though the cat is reabsorbing the kittens! I think it happens as the babies start to 'engage' in the uterus.
A lot of queens will go off their feed 12 hours before delivering. Some of my big fat girls go on eating till the first labour pain!!
My cats live as household pets so the Tom is always around the kittens. He is an important 'coach' to the new mom as he seems to sit beside her and keep her company. When I first started breeding cats, I was told to always keep the tom away from the kittens. Many years ago, when my first queen delivered, I was not expecting it yet. I came into the house to find the tom cat licking the queen's forehead as she was in labour. After witnessing that scene, I would never break up the family unit. Having said that, PLEASE do be careful if you do not trust your tom.
What is really ironic is that I have two full age breeding Toms in the household. One of them is only capable of producing certain colours so I know whose kittens they are. Both toms clean, play and babysit all the kittens. Persians are very gentle souls.