A four week old puppy is not ready to be fully house trained yet. Keep an x-pen in the house with newspapers and clean it frequently. Put another x-pen outside in an area that NO OTHER DOG are running in, and put your puppy in the x-pen, and let her play with toys, and sit out there with her. When she does potty -- set this up by taking her out after she wakes up, every time, and after she eats, etc., when she does potty outside, tell her what a good puppy she is and giver her a small piece of cheese. Do not expect her to really get it yet.
No walks at 4 weeks. Sorry. Your puppy is not safe, not vaccinated and even after it is vaccinated, it won't be protected, you need to wait on that.
She ought to sleep a LOT, and she should not be alone much. I would put a big stuffed toy in her area that she can snuggle against.
Is there anyway you can return her for a few more weeks. Only in the most dire circumstances -- dam and siblings perished, that a pup should be raised away from them at this age. They can teach your pup stuff you will have a terrible time teaching her.
Jenna, RN CGC & Babs, CD RA CGC HIC
Heidi, RA CGC
SG3 Odessa, SchH1, Kkl1, AD
Ninja, RN CGC & Milla, RN CGC
Joy, Star Puppy, RN CGC
Dolly CGC & Bear CGC
Hepzibah & Hannah