My boys get pretty hyper after bathtime...I like the term "zoomies", britster! It's totally normal. My boys do the whole digging thing...they'll rub themselves up against the couches, all over the floor, etc...for them, they're drying themselves.
For the nail cutting, let them go out and run on pavement for a while...it will file down their nails. you could also take a nail file and do it yourself, but I prefer to take my boys outside.
For the biting, I found that if your baby bites, just pull back and say "ouch!" suddenly and firmly. They'll quickly understand that they hurt you, and when you are sad at your Yorkie, they will feel SOOOO terrible! If that doesn't work, you could pop them on the nose every time they bite, they'll get the picture quickly with that too.
I wish you luck with everything, and I'm sure your baby is just fine
