Puppies can eat as much as they want and eat often! It all depends on their age. Puppies should have puppy food until they are 1yr old.
8wk old puppies should eat at least 4 times a day. They can eat as much as they want. Sometimes they are so small, large kibble is hard for them to eat. They may need small dry kibble and canned food helps as well. If you can leave food down at all times for them, that is great. But most of us have other dogs and that is not an option. You can find a special space for them, like another room or a kennel, where their food is kept. Then you can let them in that area several times a day to eat. Or set their food down and pick it up 4 times a day.
By the time they are 16wks old, puppies should be able to eat two times a day. They can still eat as much as they want, so setting down a big bowl at each feeding is ideal.
When feeding your puppy just after adoption, it is a good idea to change them to the food you will be feeding them over a 4 day period. Give them a bowl of food with 1/4 new food and 3/4 old food the first day. The second day 1/2 and 1/2. The third day 3/4 new food and 1/4 old food. By the fourth day you will have switched them over to the new food. Adding yogurt to their food will help their tummies just like it does for us humans. Just a teaspoon once a day should do the trick.
We don’t always have the luxury of having access to their old food or even knowing what they were on. So you may have to just start on a new puppy food. It would be a good idea to give them yogurt as well to help their tummies.
It is totally normal for a puppy to have loose stool when coming into a new home. They have lots of activity, stress, and usually a new diet. If they have liquid diarrhea or bloody stool, that is a problem and should be addressed either by calling the rescue you adopted them from or just getting them straight to the vet. Their stool should be solid within the week and the adjustment period is over.