If you are doing it through a private sale then you definitely need to have a 3rd party do some research and provide you info. 

Managing expectation of all parties to the deal and being transparent builds relationships (Family or not).

One month before the scheduled end of the lease between these parties onthe said property (including any extensions as provided in writing by the Owner) andprovided the lease between the parties for the same property is not and has not been indefault, an Option to Purchase Agreement for the subject property will be granted inwriting and delivered to the lessees.

Most of the other auctions went for assessed value or over.Did the 3rd party bidder just get lucky or are there some other factors that I'm missing?

If you want to avoid realtor fees, you'll need to have an real estate attorney or a settlement company attorney (also a real estate attorney) draw up the terms for the seller financing and the purchase contract along with the note and mortgage documents that will be made and signed by both parties at closing.

Thats seems fair as either party can simply vary the option terms e.g. reduce or increase monthly lease.

The records are all public record but your end buyer will most likely want a report from a certified title examiner (and 3rd party) for their own security.

The hardest part is finding the deal and getting it under contract. 

Instead, lend as a separate but affiliated party.

I will provide them a recent bank statement showing a balance greater than $300,000 and offer to pay a year of HOA fees in advance, and I will offer to have a third party investigator do a background check on me to prove that I do not have a criminal record, given that I am paying cash there is no logical legal reason why they should refuse my application, but this application process may have little to with the law.