Did the Plebians and Patricians have a war?

No the conflicts between patricians and plebeians did not lead to civil wars. The Conflict of the Orders between patricians and plebeians ended in the mid-3rd century BC. The Roman civil wars stared in the 1st century BC. The civil wars involved a conflict between the populares, a political faction which supported the cause of the poor, and the optimates, a conservative political faction which supported the interests of the aristocracy. They also involved personal rivalries.