What are these parts & how do I test them?

I got my pictures out of order so sorry about calling the first one a voltage regulator. I knew it.

Anyway, I know that the starter relay will not fire the starter with a screw driver. I tried it already. But, I am not sure if all the wiring is done right on the clutch pedal safety switch. So let me jump that connection and try again or should I just go buy a starter relay and them jump that safety switch connection?

Going by the new information, I would say you most likely have a bad starter relay, unless the neutral safety switch connection or switch is not functioning properly. As mentioned by 67Dart273, you can just take a jumper wire, connect to that terminal on the starter relay and the other end to ground. I wouldn't buy a starter without verifying it's bad. Most of the part stores can test your old starter for you to see if it is bad, or you can do it yourself with jumper cables.