Current HBS RC here who was in your shoes just a year ago
Regarding the "is it better to interview on campus" question: if you have not had the opportunity to sit in on a class yet, yes interview on campus if you can, and sit in on a class *before* your interview.
Dee Leopold repeatedly says all the time in in-person admission presentations that she's trying to find people who will be a good fit here at HBS, and specifically who will work well in the case method environment. The case method is her practically her cause. Having the opportunity to sit in on a class here at HBS, observe it, and then talk about it in your interview and how you're a fit in that classroom environment I definitely would consider beneficial to your admission chances.
If you've already sat in on a class, then I'd say it truly doesn't matter on campus versus off. The admissions department is pretty honest about their wishes so if they say they don't care then I believe they don't care.