this is totally normal behaviour.
Their mouths are like our hands so everything goes in it.
They are also teething.
Plenty of chew toys is needed and every time it reaches for your hands or clothes you need to divert it's attention to a toy.
When one puppy is bitten too hard by another then the puppy yelps and normally walks off. So the biter has no friend to play with. If a puppy bites me I yelp like a hurt puppy and end contact with the puppy. I go and get one of it's many toys and use that to play with it.
Some puppies are more mouthy than others so keep the play levels sensible and always use toys to interact.
Yes your older dog is likely to give it a good lesson on getting lost and that is normal too. Just give it some time away from puppy so it is not pushed too far.