I am sorry to hear you are so worried about Trixie. My name is Rebecca. I am a veterinarian and will do my best to help.
There are many things that can cause lethargy, weight loss, vomiting, and bloody stools in older dogs: pancreatitis, inflammatory bowel disease, liver disease, infections, parasites and (unfortunately) cancer.
The sitting and staring could indeed be old age/senility but things like liver disease and cancer can affect mental alertness as well.
I can understand your not wanting to do a lot of tests that may or may not tell you what is wrong with her, or might tell you that she has something that is not treatable like cancer. But, without doing tests we can't know for certain what is wrong with her.
Since she still has an appetite, you could try feeding her bland, low fat foods. The Pedialyte, or broth, is a good way to keep her hydrated.
You could give her 1/4th of a Pepcid AC (famotidine) twice daily; that might help with nausea, vomiting, and appetite.
Please let me know if this is helpful, and what other questions you have. Rebecca