I dayhike there and have never gotten a permit (other than a private rafting trip 16 years after requesting the permit!).
But I know about:
2. When you reach the top of the North Rim at the N. Kaibab, are there good views of the canyon nearby? Only ask because all the videos I watched show the view obscured by trees.
The expansive views are on the South Rim and some remote locations along the North Rim. At the North Kaibab trailhead, you're in a pine forest, looking down the upper reaches of a river canyon. The kind of views you imagine from the Rim were from the South Rim. And it's not like you can walk another 100 meters or a mile to see those views. The whole developed portion of the North Rim is not on the edge of a big overlook like the South Rim is.
3. Should I expect temperatures at Cottonwood and Indian Garden 15 degrees warmer than the South Rim at night?
Almost everywhere, temps decrease 3.5F per 1000 feet of elevation gain, so River to Rim should be an 18F increase. EXCEPT, in the Grand Canyon, on a sunny day, you have very hot rocks (hotter than the air temp) radiating heat at you in the Inner Canyon (below Indian Gardens), very little shade, and only the water you've carried on your back. Physiologically, I find Inner Canyon temps >30F warmer and Indian Garden temps to be 20F wamer than the South Rim PLUS the normal temp rise each day.
Therefore, you can leave the South Rim when it is 30F and be in a sweater and long pants but shed them in one mile, strip to shorts and t-shirt an hour later and be left wondering why you brought all these clothes with you when you're in the Inner Canyon experiencing 90F plus radiant input in the mid-afternoon. I graciously let my 11-year-old son do just that last May because I was along to carry it all extra clothing the rest of the day and it seemed a "teachable moment" about the adiabetic expansion of air ("lapse rate") and clothing strategies while on long hikes.