My Daisy is still a puppy as well. For teething, I have been giving her pig ears to chew on, and those have helped keep her away from shoes and furniture. They are not my favorite type of chew, but she likes them. They last quite awhile and keep her busy. I also give her an ice cube now and then. I read somewhere that ice was great for teething puppies, and she really seems to like it. She also has fun sliding it along the floor when she isn't chewing it.
We are still working on housebreaking, and experiencing accidents. I am also working on trying to keep her to a more confined area where I can watch her, as Piper's Mom suggested, but Daisy is quick. For example, I let her outside in the morning. Then she comes in to eat breakfast. I turn my attention away for a minute and she has left me a surprise in the next room. I realize now that I need to let her out before and RIGHT AFTER eating.
Regarding the rain, my older do hated getting rained on. He would refuse to do his business then come inside, and have an accident. It does not rain too often where I am, but when it does, I take him out to a planter area that is somewhat covered and watch him to make sure that he has done his business. He knows that he can't come inside if he doesn't do his job. You might look for, or create, a covered area for your puppy to go in bad weather.
