The CT scan will show you images of abnormal growths, if there are any.
The PET scan will tell you which cells in the body are multiplying very fast. This can be used to deduce if there are cancerous cells in the body, as these cells normally multiply very fast.
The fluid in your mom's lungs could be due to other reasons. TB, as her doctor said earlier, or maybe because she had been confined to her bed for too long, and developed respiratory problems that caused water to enter her lungs.
Do check with the doctor which stage your mom's cancer is at. Ask him about the histology report (the report from the lab where they tested the tumor).
Will she be getting more chemo? Not clear on her plan, also was there actually TB, and was the fliud in the lungs or around the outside. Best wishes.
There are two tests to see if the cancer has been spread or not. One test is CT Scan. The other is PT scan. They will show if cancer is there. Yes, it can go to the lungs.
Good luck.