The car does indeed start up... sometimes.
Every so often, I'll drive it around places (I never turn it off until it's at operating temp), and then park it. Then, sometimes when I go to start it up. It doesn't do anything. Everything gets electricity and everything else works. I end up having to use a long screw driver or a hammer and just tap the starter; then it starts up right away.

Is my starter going bad or the pinion thiny inside of it going bad?

 

Try checking your connections. Is the battery post clean? Next time it does this try moving the wires and see if that will cause it to start. But make sure your connections are not dirty!

 

My connections are clean, very contacting. Everything gets power. Occasionally, I get a weird noise from the starter like it's trying to do something.

 

Sounds like the starter, sometimes it's just the brushes on the motor.

 

So... Should I just clean everything inside of the starter or resort to just buying a whole new one. Brother (has FD) has told me to just replace it.

 

listen to your brother.

 

the Starter on an FC takes about 15minutes TOPS to change out..just make sure you Remember where the wires are located.One wire is sort of hidden.it is attached to the Starter wiith a Long Bolt,that goes through the Rear housing and the starter Itself.It holds a Ground Wire..It is Overlooked sometimes on REinstalling the starter.Also a Good Idea is to disconnect the Battery BEFORE working on the car.,,MARK the positive battery Cable With RED tape..In the Future you do not have to worry about Connecting the battry in Reverse Polarity..(another Common mistake).Good luck.