The plan is to Refinance after a year, applying what is pulled out, back to the mostgage to pay it off as quick as posble.

You will have to pay tax on the depreciation recapture and gain on sale (if applicable).

The investor generally needs 6 months of "reserves" or savings of mortgage, property taxes and insurance (and HOA if applicable).

But imagine you don't pay cash but rather borrow so your 5k cash/closing-down payment to buy a 100k STR, then in year 1 it rises 2k - only a paltry 2%, but you make a 40% profit as you are levered 20:1, and that beats the best year for stocks ever. 

They are yet to pay the deposit.

Does it being in at least $7,200/mo in rent to cover 1.2% DSCR loan if you put $275k down and the insurance/property taxes/utilities are under $500/mo?

If you need financial help, ask under the "Finance, Tax, and Legal" forum.

To really reap the benefits of your ownership of the NY property over the years you'll want to sell and do a 1031 exchange whilch will allow you to reposition your real estate anywhere in the country and into any type of investment real estate --- without having to pay tax on the profit from your sale or the recapture of depreciation. 

If they’re paying 85% cash, like from a 1031 exchange you have almost zero risk and 6% is fine.

With regards to the cost to step foot into this loan I’d be paying the 5,000 she has in equity plus the difference in purchase price to sale price ?