Sounds like a typical puppy
I recommend taking her to a puppy obedience class, one of the single most helpful things that I do with all of my pups. It helps you and the dog to learn work together and you get to learn all about how to best socialize the dog.
The chewing you need to address by providing her with lots of appropriate things for her to play with and chew on. If she has something that is not hers to chew on tell her "no" and redirect her attention to an appropriate item. When she switches to the toy you are offering praise her loads. Also try to keep inappropriate things beyond her reach as much as possible.
The process of house training can be a long one…pups do not have full control of their little systems until about 8 or so months. Crate training really helps with potty training.
Here is a link for you: http://www.inch.com/~dogs/cratetraining.html
The tugging on the babies diaper I would also redirect…can you give a description of what usually happens when this occurs?