Getting to a general internest is the first step. It is difficult to say exactly what the next course is without knowing exactly what the mass was.
All the questions you asked above are reasonable questions - about surveillence, work restrictions, diet changes etc.
I would also inquire about what was found on the pathology, whether any chemotherapy/radiation therapy is needed.
About surveillence, you can also ask whether periodic upper endoscopies or CT scanning is needed to ensure the tumor doesn't recur.
Seeing the interest can guide you to an appropriate hematology/oncology specialist where further follow-up can be arranged.
Followup with your personal physician is essential.
This answer is not intended as and does not substitute for medical advice - the information presented is for patient education only. Please see your personal physician for further evaluation of your individual case.
What you describe sounds like a leimyoma, which is a benign tumor originating from the muscle layer of the stomach. It's in fact not rare that they present on the outside of the stomach. They aren't dangerous like cancer, but they can cause erosions of the lining, or sometimes can lose blood supply and start to die which can cause, among other things, pain. If that's what it was, then removal is all the treatment you need, and there's really no need for surveillance or other treatment. Of course, you need to know exactly what was found: even though it sounds like the surgeon was unfortunately brief with you, I'd assume that if it were another sort of tumor, he'd have told you about other postop needs.
Most people end up eating virtually normally with no digestive after-effects when half the stomach is removed. But, depending on how things were done, it's possible to develop what's called "dumping syndrome'" which results from losing the control muscle at the bottom end of the stomach, which allows foods to get into the intestine faster than normal. Especially when the foods are high sugar and liquid (the worst being a milkshake, for example) as the food moves into the gut there can be cramps, diarrhea, nausea, sweating. There are various ways to deal with it.
I'd suggest seeing a gastroenterologist rather than a general internist, although I'm sure there are many who are comfortable dealing with dumping syndrome. I'd also point out that this early after surgery it's possible there's some sort of postop infection going on inside. I'd also suggest seeing the surgeon again to get his input on what's going on. It's one thing to dismiss you after a week assuming everything is ok: but when it's not, it's his obligation to see it through with you. If it were me, I'd probably be ordering some blood work and possibly a CT scan, just to rule out an abscess or other postop situation.
You absolutely must find you an excellent doctor to do some followup with you. It seems to me everything about your digestion would change if half your stomach was removed. Please act quickly. You are lucky that you have good medical insurance. Use it to find a doctor who will give you the answers you need and deserve.