I can't believe your being told to keep a pup fat. Keep it healthy.
And it's fine to take a pup away after 5 weeks especially if it's going to get plenty of human contact.
And at that age meat is fine if it's the right sort of meat. I cut tripe up fine for pups from 5 weeks on, minced would be better.
Remember when changing any dogs diet young or old, do it gradually.
A fat pup can be a sign of a wormy pup.