If buyer requests repairs and closing costs, does this give buyer option to terminate contract if seller does not agree to closing costs?

Sorry to give a wishy-washy answer but it all depends upon how the contract is worded so you need to have an attorney review the contract, assuming it is fully signed.  If you are still in the negotiating stage, it sounds like you received a counter-offer, which serves to reject any offer previously made by you and you could simply reject the counter-offer. Let a lawyer read the documents to get an accurate answer.