As long as you have clearance and it doesn't touch the cooler you should be fine to mount it behind just fine. If it can touch and vibrate against it you run the risk of it eventually wearing a hole in the cooler, which would be not good.
My first thought is when was the transmission oil changed last? I was starting to get some of those same things going on until I changed the fluid and now it is all better.
I used the remote wire from my radio to power the relay for my KC lights. That is inside the cabin though. The headlights might have a lead that is always Hot when the ignition is on, but without checking it with a voltmeter I would have no idea.
I am at 98k with my '06 and I am definatly starting to get the "supercharger" whine noise most noticable at slow speeds from those stupid chain tensioners wearing out. It is a design flaw with the 4.0L engine that I wish Nissan would address. My local shop quoted 13 hours of labor plus par...
With an auto tranny your probably doing the best you can get with 4Low. Otherwise 4High with light braking is probably the best alternative, which you are already doing.