Validity of Agreement of sale

We are about to purchase a land from the party, herein ‘seller’ which is already under an agreement with another party herein ‘buyer’ from 26/08/2017. The validity clause of the agreement says that the agreement shall stand valid till the expiration of 6 months and any default shall give the right to the company to terminate the agreement without any prior information. “A clause of an agreement says that on the default of the payment for more than 6 months the Company shall hold the rights to terminate the agreement without any prior information.” Now, in the instant case, the party entered into an agreement on 26/08/2017 with some token amount and has agreed to pay the monthly installments within six months but the buyer has defaulted to pay the amount within six months. Therefore, as per the agreement, the validity of the contract has ended on 26/02/2018. There are some issues on which I seek to get an advice on this matter: 1. Even after stipulation of time for the validity of the contract. Does the buyer have any rights in respect of an agreement? 2. If the third party has purchased the land seeing that the earlier agreement has already been expired. Is there any liability on the third party? 3. Does it make any difference if the agreement to sell is not registered?