I handle my pups as soon as they are born, Children do carry a bunch of germs from friends at school , but after they were a few weeks old as long as they washed there hands and were not sick them selves I think it is okay.
I start feeding mine at 4 weeks with ground up dry puppy food and puppy formula.
In winter I use the heating pad all the time on medium, in one corner of the whelping box.
As far as vaccines, my new vet won't do them until 8 weeks, which is just fine with me..
I think it depends on the size and state of the puppy, as to when they should leave the nest.