@Jason Riddle you have a good post above already. I'll try to add a little here:
1) Is it possible that the seller would accept a lower interest rate than the market rate? If so, why would they do this? - There are all sorts of reasons "why" someone might do this and sometimes we may not know "why". It is not common...but it is possible (but it is rare).
2) Would the seller also accept a lower down payment than 20%? If so, why would they do this, since this increases their risk right? - Same here, it is possible, it is rare, they aren't usually thinking about "risk".
3) Why would a seller ever agree to this? It seems like a bigger headache to manage a loan? What are some of the dire situations they would agree to doing this? - Well, this isn't really your problem. This is their loan. You don't really worry about Bank of America and their position, right? Same thing here. If they choose to go this route, the responsibility is theirs.
4) Would the seller provide me monthly mortgage statements? If I wanted to pay down the principle quickly, is this possible? - If it's a sophisticated lender, then yes, they would provide you with monthly statements. But for the scenario you seem to be describing, it sounds more like someone who is not sophisticated - and then you will have a little more responsibility of tracking your payments. Sometimes owner financers don't even provide a 1098 for us at the end of the year...and we have to generate (and track) our own tax deductible interest. Usually the better the terms, the less support you receive.
5) Would I put the seller down as the mortgagee on my homeowners insurance? Would they also collect escrow for taxes and insurance? - Again, this is NOT your responsibility. This is theirs. If they don't require you to put them as a mortgagee on their insurance...then that's to your benefit. It's not to THEIR benefit...but it's to your benefit. Same with the taxes and insurance. That's on them. Requiring an inexperienced person to use a mortgage servicer might actually backfire. They may not be savvy enough to understand what that is nor have any interest in making their loan to you more complicated. All of that is on them.
Hope some of that makes sense.