I believe there is a table to be filled out to answer this questions. For certain results, I think it's better if you will perform the procedure. But I'll help you out with the questions, don't worry.
Q3. The answer for here depends on the data results. It depends on which is your dominant hand. Your dominant hand is the hand that you usually use on writing, holding/lifting objects and etc. Like me, I'm right-handed so that is my dominant hand. Your dominant hand (right or left) will catch the object faster when your eyes were open.
Q4. Same goes with Q3, your dominant hand usually catches the ruler faster.
Q5. Ah that depends also on which sense organ works the best. Sense of sight or sense of touch. Catching the ruler with your eyes close depends if your teacher allowed you to make go signals such as: 1,2,3 GO! (Our teacher allowed us), since we can hear go signals, it is much more faster for me to catch the ruler. Because my sense of hearing is better than my sense of sight. But if your teacher didn't allowed you to do that then it is faster to catch the ruler with your eyes open.
Q6. Because of nerve cells handling its information to the next cell, which passes the information to another.
Q7. The receptor/your eye saw the ruler fall, so the sensory neurons of the receptor receives the information, the information will be sent to the brain then it gave a response to your motor neurons to command your fingers to catch the ruler.