Then when we were granted eviction all parties would be removed from the unit and we changed locks on all doors right away and secured.

This allows me to close sooner than the date listed if all parties are in agreement.

I'm looking at a property from a third party.

The hard part is done, finding the deal. 

Both parties must sign for the property to be sold, and if you do take a Gurus advice, I suggest the seller to don't spend the money just in case if someone came calling they might call that mortgage fraud.Joe Gore

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.