I would contact the seller and point out the issue....as well as the inspector........and sternly request to be reimbursed...more so from the inspector, since I think more liability falls on them.....the inspectors I have worked with kick on the heat and a/c for 10-20 minutes and actually see how they work to cool/heat the house......be stern but polite and respectful.

The tenant buyer will pay a higher rent, they will give you a downpayment non-reimbursable and they will pay x price or the Fair Market Value at the time of closure - whichever is greater.

I might offer to reimburse attorney at close.

You will not be reimbursed for your labor.

I don't want to use them for the rehab as I will be doing some of the work myself and I'm not a licensed contractor so getting reimbursed with draws wouldn't work. 

To actually finish a project, I'd recommend setting aside at least 6 months of interest payments and 10-20% of the rehab cost (since you'll be fronting the money to start the rehab before getting reimbursements). 

Mileage reimbursements for visiting properties and driving for dollars, 

I usually reserve that threat for after I am told “no” on my polite demand for reimbursement.

Should I offer to reimburse them  $300 for their inspection ?

I do want to get something in writing that says that the tenant will not be reimbursed in any form or fashion for his half of the cost.