The wire snapped on this connection that goes to the engine block, but I have no idea what it is and what to ask for at the mazda parts counter. Any ideas? And do I need to buy a part or can i just wire it directly to the engine with out that plastic box with all the funky numbers?

 

Thats a resistor for ummm something

There's a few of them in the engine bay and each serves a different circuit. I *believe* the one under the clutch slave is for the oil pressure sensor...

I would look around for some in the junkyard, or find the part number in the FSM so the dealer doesn't order 67 other pieces trying to gt what you're after.