If there's already one on the truck, then you are 90% there. The one thing that you might need to do is "tune" the antenna. You'll need to either buy or borrow a SWR meter to do so. This will make sure the antenna is the correct length.
You are likely correct. Although I've had a few vehicles where the accessory plug has power all the time. I'm very tempted to add an additional "always on" plug to my current vehicle as all of the ones in it shut off with the vehicle.
When I first posted, I only saw your first picture. I now see that you have an adapter plug on the back of the unit with three wires. Is there already a place on the truck where this would plug into? It would be something that was added on, not standard with the truck. If not, this adapter setup is likely what you'd need.
Correction: that's not quite what you'd need, but it's very close and would likely work if you are ok with doing some rewiring. It looks like the original 3 pin end on yours was replaced at some point with a 4 pin end, with one pin just not used.
You are welcome.