[PeteKz]

That looks like the right terminal (no guarantees!). I'd order several of them, because there are a handful of them in the engine bay, and you might need to replace others some day.

Re the burnt wires: Those tend to get hotter at their connector ends because that's where the highest resistance is. I've seen many wiring harnesses where the insulation was melted at and near the connector, but still ok inside the harness. Open the 14 pin connector on the engine wiring harness and see if the red/white wire is melted there. If not, put it back together, put on a new connector and run it. You could also do a continuity check between the other wires in the harness at the 14 pin connector, and if you don't have any shorts from that wire to others, make a note of what happened, but leave it alone. You are likely to cause more problems by pulling the harness apart.

Yes, you can bypass the red/white wire and the brown wire--that wire should be brown for ground, not black. the brown wires are grounded at several points, including on the engine. If you feel that you must bypass the melted wires, then the red/white wire carries power when the ignition switch is on to all the CIS component on the engine, and the brown wire carries the current to ground. Any ground point on the engine or chassis will do.
As far as soldering and crimping technique, there are plenty of YouTube videos on how to do it. Look at those.