Electrical System Flunked

Here's what I see.
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The big cable to the starter is only important for starting. It does nothing else.
One of the red wires with a ? should lead to the starter relay. That's the original main battery feed. Find it.
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Connected to the same stud on the starter relay should be another wire. Remove the wrapping if any, and follow it.
It also was red but will have a short blue wire (fusible link) somewhere in it. It should lead to the firewall. Probably to the multi-connector.
Since there are extra red wires on the battery clamp, you might want to follow them to see where they go. It all depends on whether you care to figure out what was hacked or just want to put it back the way it should be.

On the alternator, it looks like the original output wire is still in place but there is a red wire added.
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The heavy black output wire should go to the firewall. In the diagram its marked R6 (R for alternator).
Remember this is all hooked to the battery so will be hot when the battery cables are reconnected.

That should get you started on tracing what should be there and where it goes.
They should connect on the inside with the power feeds to the key switch, hot side of the fuse box and headlight switch.
When the engine is running power comes from the alternator. When the engine is starting or alternator can't provide, power comes from the battery. Pretty simple.