Check your engine mounts, the one on the front tears easily as does the one on the rear. The one on the passenger side is filled with a fluid and leaks are common.

I learned to rebuild transmissions as an apprentice in a dealership.

Yes. They’re just gears and the fluid degrades with time and heat. (the front differential is actually in the transmission, and you should change its fluid too )

It’s used for adaptive cruise and collision warnings. It’s not essential, but as a safety device you will have a warning on the dash.

Remove the wire tire from the stud. Or just pull the harness enough to get the stud out of the bracket then take the bracket off the plenum.

That’s a heater core getting clogged. I did one last month on a Jeep Liberty (cousin of the Nitro). It cost about $200 in parts and 7.5hr labor.

It could be one of the axle shafts. You can download a vibration analyzer app on a smartphone or tablet to tell you what frequency the vibration has and then determine what part is most likely causing it.

Flush would grind, gap is good