i have started weaning my hand reared puppies at 3 and half weeks old , they love the food but after 2 hrs have passed they start to vomit some of it back, is it safe for them to lap water out of a small dish

I would imagine they have eaten to fast and ate too much I would only expect them to eat a small amount in the early days of weaning , and yes they can lap water if they want ...remember to use a shallow bowl and be careful none of them can fall in it as it only takes a small amount of water for a puppy to drown.