Sounds as though you are doing everything right, and with good consequences, and there's nothing to worry about. With a pup it's desirable to moisten the dry food with something because they may not take to it dry even though there's water provided (as the makers always say there must be). If you mix the dry food with the 'wet' food that moistens the dry a bit and the pup will then do as it's doing, eat it all.
I haven't quite understood what you mean by white line. The pup may have darkish nails which have a white tip. That's normal . If you wait,as the nail grows the white bit gets longer.Is it this that you mean? You have to be VERY careful when filing or cutting the nail. The dark line in it is the 'quick' which may be very difficult to identify in some nails. If you cut into the quick by mistake the dog will be in pain (and will run a mile every time it sees you approaching with scissors , ever after! ).It may even be, in this case, that it's the living quick part of the nail that you are seeing but without seeing the pup,of course, I can't tell.Best leave intial trimming of nails to a vet or professional groomer who will show you