I applied and thought long and hard about going there. It's an amazing program, arguably (probably?) the #1 healthcare-related MBA program out there... unparalleled reputation if you're looking at hospital administration, big pharma/medical devices, or healthcare-related IB/PE/MC. Also very good for earlier-stage ventures and VC. As an added bonus, HCM students form a very tight-knit group within the larger Wharton population. A really great bunch of people.
Essays- You just have to make a good case for why you want to do the HCM program, and how it fits with your goals. Most applicants tackle this one in essay 1 ("Why MBA, why Wharton, why now?"). A healthcare background isn't necessary as long as you're able to explain why you want to do the program. I think you have a bit of background in the field, though, so that last point is moot.
Interviews- You have two interviews. I believe the same percentage of HCM applicants (~40%) are interviewed as in the general applicant pool. One interview's with the usual Adcom/student/alum, the other's with June Kinney. June runs the program and is one of the nicest people you'll ever meet. Ideally you'd interview on campus so you could meet June in person; if you're unable to get to Philly, though, I know she does phone interviews as well. The interview with June is really a conversation... I think she wants to make sure you understand the program, and that you'd be a good fit with the rest of the group.
June's very amenable to people reaching out to her via email/phone in the summer and early fall to talk about the program and ask questions. It's a good way to get a feel for the program, and to introduce yourself to June. I wouldn't do it now (it's early, and I think June's still dealing with R3 and WL), but keep it in mind for later. Just google "Wharton HCM" and you should be able to find her contact info. There's also a bunch of great info about coursework, etc. on the HCM website that should help you formulate some good ideas and write effective essays : )
Hope this helps!