Good that you have her in your care. Things you can do are:
1) Take her to the vet for a complete physical - CBC and urine. Make your appt early in the am, don't feed after the night before (only water). Get a stool sample (even the night before), put in a baggie and refrigerate. Do not allow to freeze. In the am, try to get a urine sample when she squats. I find a top of a plastic disposable container works best. If she squats low (lots of females do) you can slip the lid under her. The first pee in the am is best. Poor it into a clean container and refrigerate til you go to the vet. It doesn't have to be much - maybe only < 1/4 cup.
I can't really see her gums in the pics. If they are white, light blue or basically anything than a nice pink color get to the vet soon. Can't remember after writing this if her temp is normal range - 100.5-102.5. Although she is thin, and needs weight obviously, this could be the least of her worries. Feed her many (4-5 small meals/day) don't load her up on one or two feedings/per day, spread them out not to overload her system. Check the conjunctive tissue in her eyes. This is the white/light beige area you see when you lift up or down her eyelids. Sort of like when you do this to your own eyes. They should be a light pink or a nice healthy white-ish, like your own. NOT gray or bluish.
As far as the "alleged" carcinoma, have your vet do a biopsy, but it could be something very normal and not cancer at all. Trust me on this one, it "could" be cancer, but maybe not. I've lost four Rotties to cancer.
Best of luck- get her to the vet, take stool and urine samples, check her baseline temp at home, feed her many small meals and hope for the best. I certainly am rooting for her and for you guys.