Contract not signed by the parties and not performed. what can we do

If the contract has been exchanged between the parties but has not been signed and one party execute its part but fails then : 1. Will other party be entitled to recover damages from the party who executed the contract without even signing . 2. Whether terms of contract will be applicable ? 3. If the process of arbitration was mentioned in the contract which was not signed between the parties yet was exchanged then invoking arbitration becomes necessary? 4. Whether the amount decided in the contract for non-performance can be demanded through recovery suit?