The Germans most likely knew that the Lusitania was carrying war supplies for the British. Did this give them the right to sink the ship? Why or why not?

Depends on how you look at it ... They were desperate and had to stop the British from gaining support. But it wasn't confirmed that It was carrying weapons, there were civilians on it so theres good reasoning why they sunk it. The Germans did not let civilian casualties get in their way really as seen with their bombing of cities and use of chemical warfare.