The property is already an STR and the current owners have bookings confirmed into July.The closing date is set for March 30th (meaning, I will then take over the property that day).The sellers have asked me to either let their pre-paid guests stay in my property (and they keep the profits)ORpay the sellers nearly $6k, in reservation fees that they would have profited if they were not selling the property.Is this common?

When you finance a purchase your "closing costs" are actually "closing costs and prepaid expenses" and typically the prepaid expenses (homeowner's insurance and property taxes) are the lion's share of the "closing costs". 

But 'closing costs' include things like pre-paids: interest, property taxes, insurance,  etc which are operating expenses.  

"The new loan amount can be no more than the actual documented amount of the borrower's initial investment in purchasing the property plus the financing of closing costs, prepaid fees, and points on the new mortgage loan (subject to the maximum https://www.fanniemae.com/content/guide/selling/b2/1.2/03.html)"

Depending on the number of calls you get, a pre-paid plan might be an option.

I would for sure have an operating and escrow account to hold deposits/prepaid rent etc. 

The 10k is 2-3% closing costs - taxes and prepaids. 

Take along an independent, prepaid inspector not party to the deal or other trusted person to actually price out the renovation and to do the work correctly, professionally, and without cutting corners or being sub par.

@Steve Vaughan Prepaid appraisal 675$ (mortgage company rates)well inspection and water testing over 1K2 Radon tests $300Septic - $450Building Inspection - $600Closer to $2400 I guess, I live in Fairfield county CT for context on pricing.

@Alexander F Pollock, I am going to give you a semi-snarky response: if security deposits could be used for rent, it would be called prepaid rent.But like others mentioned: no.