Starter Relay Wiring
You might be able to salvage the wiring, but seriously, you need to just undo everything at this point and start with a CORRECT diagram. (See below) For your pix, with the ballast and regulator tied to the big post on the relay, the ignition system looks to be ON anytime the battery is hooked up. Does this car have the stock ignition switch in place or other switches? Is this a drag car only?
For stock wiring: Be aware that there are 3 ignition related wires in this area: 1 is the main power feed into the whole dash, and 2 out of the ignition switch called IGN 1 and IGN 2. The main power feed into the dash area is likely the one going to the big post on the relay. IGN 2 feeds 12v to the starter relay and to the brown wire going to one terminal of the ballast the ballast. IGN 1, feeds a blue to the other side of the ballast, to the ECU, and also to the regulator and to one of the field terminals on the alternator.
What I described above is for a real 1972 or later Mopar system. YOUR DIAGRAM is for a 1969 or earlier system so is not what you want to follow if there are 2 small wires + 1 big wire on the back of the alternator. And your diagram is also not right for the Mopar ECU ignition system.
You need to tell us your ignition system and the number and sizes of wires on the back of the alternator. Plus if this is a street car or for drag race only, or what...
As for as how to fix this? With wires cut so badly, it would be wisest to start from scratch, IMO. I'd bet the bulkhead connectors are half bad, and who knows how badly the dash area has been hacked. Hence the fire comment above...