I wouldn't worry about her weight. She's at a normal weight for her age and because she's a baby her weight will change a lot within the next few months.
As for her hair, my one yorkie Bella always has tangles because her hair is more cotton then my other Yorkie whose hair is really silky. It's just the type of hair she has (maybe get a leave in conditioner or detangler) and make sure you brush her hair every day so the tangles don't get out of control. If you really want to get her groomed i would stay with her if you can because she is kind of young but you said it's really cold where you are so i wouldn't get her groomed until it worms up a little so she can keep her winter coat for warmth.
Try and make her bath times fun and maybe just put a little water in the sink at first and let her get use to her feet/legs getting wet.
To keep the clothes on, at first i would put a shirt on them and then put on their harness so they wouldn't be able to get their legs out of their shirt. They would get use to their harness at the same time. Eventually i wouldn't put their harness on over their clothes and they would leave their clothes on.
Good luck
