Hi - welcome and CONGRATS!
Puppies may have excess eye drainage due to teething, so that may be what you're seeing. Also, some dogs just have more discharge naturally. You just need to watch for it being greenish, which could mean an eye infection.
Some flaking/dandruff is pretty normal w/ pups too. You could try adding a bit of coconut oil or fish oil to the diet.
As for grooming, it's really impossible to know if someone will hurt your yorkie, to be honest...this is why I do all the grooming myself for my kiddos - I don't want them put at risk or vulnerable to a stranger like that.