On the numerous other homes that were around the same price point that we submitted offers on prior to purchasing this one, our EMD was $500-$1500.

In Florida auctions, the 5% needs to be in the Clerk's account prior to bidding, then the remainder of the bid price plus Clerk's Fees, Doc Stamps, etc need to paid by noon the following day.  

My mother asked me about what happens when the previous owner (prior to me) has a mortgage on the property.

I had to wire the money to the closing attorney, but they actually sent me the wrong wiring instructions.

I have very little experience with prior deals, but am trying to extend my network with hopes of doing something in the SFR space by year end.

The only way to get it reduced, is find the prior owner offer them some money to sign a quit claim deed on the property.Your second is a grey area for Dallas (liberal Judges).

Then you rent out at or just below market to get tenants quickly after carefully screening your tenants - including criminal check, credit check, calling prior landlord (or two) and calling employer.  

Prior to purchasing these properties, I struggled with the question of buying locally or remotely. 

Heck, I was accused of giving terrible advice when I posted it in a thread in which the landlord was being given instruction by the tenant as to when the landlord could access her property!  

Though the home is a foreclosure, who were they paying rent to prior to you purchasing?