'68 Dodge Dart: Two openings in trans tunnel 4-speed manual

That white wire attached to the screw looks like a 110v electrical zip cord.

You are right but idk yet what it is for.

That is where the linkage for an automatic transmission goes. The hump where you shifter is is correct for your car, do not worry about the other one. Seal it up so moisture & critters can't get in & you are good to go.

That sounds not as bad as i thought. Do you know if this was done by a previous owner or is the opening for auto there from the factory and they just fitted the correct tranny?

Look in the service manual in the automatic section, it will show the auto shifter setup for console. Are you CERTAIN the fender tag matches your car?

I checked once again and VIN tag, fender tag and broadcast sheet match and all say 4 spd manual.