To answer your questions, I understand that rats become sexually mature between 6-8 weeks. I haven't really paid close attention, but that would be my estimate. Yes, it's ok to foster rat pups to other moms. They will generally take them in no problem. I don't know about separating by sex at birth, but you could do so after a couple weeks.
The mother rats will take care of the pups and will wean them. You'll notice at about 4-5 weeks, the rat pups will start eating the solid food and drinking from the water bottle. They could probably be separated from the moms at that point, but I've also heard to wait until at least week 6, but if they're just getting fed right off, there's no hard and fast rule. I typically feed when the rats are 50-75 grams, so technically probably considered small rats. I have some bigger girls who could take bigger meals, but I prefer to feed two smaller rats that pose a smaller threat to the snakes (since I feed live).