Can I include any of these in the property "basis" when figuring capital gains?
my closing costs (broker fees, title company fees) etc
Closing costs that cannot be expensed are added to the basis.
closing costs amount paid to buyer
This is essentially a discount on price, so yes - it is added to the basis.
apportioned amount for year's county taxes, month's HOA fees etc
These cannot be added to the basis since these are expenses. This are not part of the property acquiring/sale costs, but part of the property maintenance/ownership costs. Since it is a vacation home - you cannot deduct them (although you may be able to deduct the county taxes on your Schedule A, if you qualify).
Also, can I include repairs the buyer asked for as part of the contract (new Water Heater, new electrical outlets)?
These are also expenses. You may want to ask a professional about the new water heater, but I would argue that replacing a broken heater is not an improvement and as such is an expense. So no, not deductible at all for vacation homes (could be for rentals), and you cannot add them to the basis.
IANAL and IANATA (I'm Not A Tax Adviser). Please consult with a EA/CPA licensed in your State to confirm.