Congratulations on your puppy.
I would say on number 4 and 5, this is part of having a Yorkie.
You'll have to watch every step you take or he could easily get hurt.
Your kids are quite young to have a dog of this size.
So he doesn't get hurt, I wouldn't leave them alone together.
Supervision will be needed at all times and rough play just can't be allowed for the pup's safety.
How about only letting the kids hold the pup while they are sitting on the floor with you right there and no running by him either?