Ok...
Couple quick notes of explanation... The unit does not come with a cord as a factory standard item and was a point of confusion that we identified before they shipped the units. They threw it in in a hurry to get things shipped. It'll work though. Notice the effective current draw. That combined with the NEC's specifications for derating their standards for duty cycle limited machines means it should be well within the standards. The I1max is a temporary start up demand not likely to heat up the wire or cause issues. Where you see it connected to the rear, that is where it was originally intended for the customer to take over. When we figured out what was going on, we asked them to put a cord on the end of the machine. Its a first shipment and there is always going to be minor issues like this. The cord is fine if you cut the plug, but I'd suggest that customers put their own on the unit, tying in at the back. Green/Yellow is the ground on this line. Other two are hot. This is a european plug. Wire is fine though. The piece of plug you have in the box WAS the original plug that was used for the orginal test design, without a foot pedal. They included it because they were going to include it anyway. The line I believe, is for installing the water line back into the unit, which we deleted...for safety concerns. Other than that, I have no idea and should have no bearing on the operation or use of the welder.
The switch missing on the rear was a last Second change quite literally before they shipped. We sent our specs on our foot pedal and they had a different one they wanted to use. Theirs needed a switch, ours do not...ours are wired so that the plug itself acts as a switch when the unit is plugged in...
Edit, yellow wire is connected internally inside. It should be screwed to the case inside...however, originally the third slot there was going to be for customer attachment of ground, but when they put the plug on it, they just went and connected directly. If you see the manual, that is how it should/would have been connected and it should still be capable if you'd like. 8 gauge is a suggestion, not a requirement. Post up pics IF you do decide to change it.