What are these parts & how do I test them?

You jumpered across the two large exposed terminals?

And this does not operate the starter?

If so, it's not the starter relay.

Might be the wire itself, the big one from the square terminal down to the starter solenoid, in any case

bad connections at or around the starter

Sometimes that solenoid wire or even the battery cable breaks internally

Or bad starter

Good point; it can't be the relay because when he jumpered it, it bypassed it and it still didn't work.