Awww Thumper was happy to meet little girl, shows how much he needs a companion. My last girl would rub her body against the sofa, turned out to be food allergy's, my vet gave her a shot,and changed her food and that stopped. I had another girl that would roll and rub her body on toys, she was marking her scent on them lol. Could be this pup is putting her scent on your things,claiming them as hers, just a thought based on my experience with my girls.
I can't say if blood work is "normal procedure at rescue/shelters" I have never had dealings with shelters/ rescue facilities. Hopefully you will get answers on that.
In my opinion, I would "think" dogs entering shelters would go through a physical with blood done "before" going to foster care to make sure dog is healthy enough to be adopted.
Sliding on hardwood floors lol, they have no traction lol, Cody does that in the kitchen, he knows he can't run around in there, she may need her nails clipped,long nail will cause sliding and slipping, you can put down some carpet runners or area rugs.
I would suggest asking the shelter if you can take her to YOUR vet for physical and blood work "before" you commit to adopting her, but doing this will free her up to be adopted before getting the results of the blood work.
Adopting a dog is like buying a used car without your mechanic checking it out, it's like a "buy as is".
__________________ Joan, mom to Cody  RIP Matese  Schnae  Kajon  Kia  forever in my  A House Is Not A Home Without A Dog |