Talk to a LOCAL lawyer and see whats required to re rent it and dispose of possessions within the law.

If, for example, I require non-subsidized prospects to pay our standard Security Deposit within two business days of application approval; and require that rent will begin being charged the earlier of 15 days from our approval, or actual possession; and that both deposit and initial rent be paid prior to occupancy, how can I be required to change those standards for subsidized prospects in order to fit with their subsidy program?

What matters to me is that they made another landlord go all the way through the formal court eviction process to recover possession of the property.  

May I suggest you write into your offer a  clause that gives you a delayed settlement with possession contingent upon a loan.

If no cancellation clause is in the lease and the lease term has not ended, they cannot legally demand possession. 

Since it is now past the redemption period the high bidder may take possession of the property immediately upon recieving the deed.So there are actually two different kind of tax deed sales even within one state.As far as a forclosure process being judicial or non judicial.

If the tenant is out and you have possession of the property, why file for eviction? 

I also hire a private process server for the 5 day notice from the court and request personal service so I can get a money judgement in addition to the writ of possession.

I know they have not been there long enough to gain "adverse possession" or squatter's rights, but all the research I've done hasn't led me to a consensus on whether or not this would require an eviction process as if there was a landlord/tenant relationship, or if I can just call the sheriff to have them removed.

If you are in title and someone else cared for the property and made mortgage payments, they can make other claims for possession and sue for costs.