Is it permissible to bet and consume from its proceeds, and is it true that a man once bet with the Messenger of Allah, may Allah’s prayers and peace be upon him, on his horses, whereupon the Messenger won and took the wager?

If the wager you witnessed was Islamically permissible, then there is no harm in your witnessing it or partaking of its proceeds. However, if it was forbidden, then it is not permissible to do so. The Prophet, peace and blessings be upon him, wrestled Rukanah and defeated him. In some narrations, he wrestled him for sheep, which he returned to him upon Rukanah's acceptance of Islam.