Could her coat just be oily/greasy because she has not had a proper diet or care while she has been out?
You are doing a great thing by taking her in the picture of her is lovely
I do agree to probably take the collar off her and get her some flea treatment from the vet.
I have been there with inspecting poo and its not nice, my little kitty had worms and she had the treatment and now all is ok, so she may need a stronger de-wormer.
Hope all is well for you and your new furbaby and you can get everything sorted