I've heard of some people putting together a binder that shows previous deals, returns, tax returns, profit and loss statements, bank balances, etc.

I would be hesitant with this specific deal because the cash flow is too minimal for my liking, and the ARV doesn't pan out. 

Is the month of the auction a loss rent month as me the new owner?

The tenant may have mentally already written it off as a loss, especially if they are used to dealing with dishonest Landlords that keep the entire deposit just because the tenant failed to clean the over.

I would try to hold the property a bit longer because of the fact that if you build up enough equity, you can then at least net 0 in the next few years as opposed to taking a flat out loss. 

If they take the land will I get at least what I put into it or take a loss?

No because it will depend on your tax bracket and whether you can claim rental income as QBI and whether you can even deduct losses from RE.

Also, being able to add “loss of rents” can be important if you are heavily reliant on the CashFlow that the tenant brings in.

For your smaller deals (less than 30 units) using a 10% vacancy/collection loss factor and a 55% expense ratio is a pretty good place to start the analysis (might be a little conservative from a V&C standpoint).

When you buy with other loans and put minimal down payment, you end up having to pay PMI which usually destroys any cashflow.