I would recommend hiring a lawyer for a non-monetary default eviction.

Basically could say im a street kid who abandoned all the ******** and people from that life two decades ago and I desired more and achieved it both in monetary and goodness.

I think I've found a property that fits my criteria at the right price, but I'm not totally sure on its ARV nor its rehab costs. 

Some investors prefer to start saving for these ASAP, while others plan to deal with them when they happen.The unknown is Maintenance costs, which are often dictated by how "hard" a tenant lives in a property.

As I am considering my offer, I am trying to understand how much to budget for attorney, title/closing costs etc? 

The cost of labor , materials , property taxes , inflation , interest rates  etc .

Now, you are asking can you use a Gap/Transactional funder for the downpayment and closing costs? 

“Inflation is always and everywhere a monetary phenomenon, in the sense that it is and can be produced only by a more rapid increase in the quantity of money than in output.” - Milton FriedmanAgreed Russel. 

https://www.biggerpockets.com/forums/51/topics/1113749-cost-segregation-faq

I'd first take it up with the eviction court and ask for a monetary judgment at that time.