Home room at my school was basically the same as @HitmanHart’s. It was for morning attendance and dealing with school paperwork like report cards and such. They were organized by alphabetical order of last name and year of graduation and had no other significance. For example, all the A-names and a few B-names from my graduating year were in my homeroom.
The only senior privilege we had was “senior study,” which allowed us to go outside near the cafeteria instead of being cooped up indoors all day long. We were also allowed to be fairly social (it was held in the school auditorium) instead of only being able to work or read quietly. There was also Senior Skip Day, but it was an unofficial privilege not endorsed by the faculty.
All “study halls” in my school were just cases where you had a free period on your schedule that wasn’t occupied by another class. For high-performing kids, it usually came as a result of odd scheduling quirks involving classes that didn’t meet every day, such as phys ed or lab sessions for science classes. I think my senior year did have an every day one, but it was because my schedule was already full with honors and AP classes, none of which fit in that time slot, and I didn’t find any interesting elective classes to fill that slot either. I think I only had any sort of study hall for two of my high school years, and one of them was the aforementioned senior study.
My high school did have shop and home ec classes, but generally those were elective classes and I didn’t really know anyone who took them except for maybe a couple of kids my senior year who wanted to pad out their schedules.