Can be. Initial symptoms of HIV infection are non-specific. You can have a runny nose, fever, cough, nausea, diarrhea, etc.
Possibly. Hiv is an immune system disorder, and our gut is the biggest immune system organ in the body. Diarrhea, cramping, and change in bowels can signal full-blown hiv. See your HIV doctor if you have one, or your primary doctor.
Depends. Some symptoms such as unexplained weight loss, chronic diarrhea, or pain with swallowing (odynophagia) may represent an opportunistic infection in a personal with HIV infection. If you have a concern about a digestive symptom and HIV infection, you should talk to your health provider about it and consider being testing for HIV infection.