Am I obligated to pay half of the speeding ticket my friend incurred with his car, given my prior knowledge of warning him not to exceed the speed limit, and would I be sinful if I don't pay it?

You are not obliged to share in paying the fine, and he has no right to demand anything from you, because fining the driver for exceeding the speed limit is a discretionary financial penalty that the doer deserves. If you wish to help him voluntarily, you will be rewarded, for the Prophet, peace and blessings be upon him, said: "The best companions in the sight of Allah are the best of them to their companion."