All NSW sales contracts have settlement periods on the front page - the same page you would have signed - that means that the settlement terms were on the offer you made and received by the vendor.
Standard is 42 days
You may have been used - you may not have - let me explain....
By the sounds of it the other purchase had made an offer that was accepted and properly signed a contract and paid a deposit - the only sticking point was the settlement period.
You become interested in the property and the...