Well, lets see if I can at least address some of the questions. Yes the NAT
tracks are the busiest. But there are also flex tracks over the North Pacific (Asia/Japan to the US/Canada), Central Pacific (Hawaii to Asia), Northern Canadian Tracks (NORs) that best i can tell are for Europe to the Western US traffic, and Australia Tracks from the East Coast cities to Southern Asia and the Indian ocean. Thes are all "flex" tracks, in that they change every day and are published at certain times. The tracks change daily based on the more favorable winds.
There are other "tracks" such as the US mainland to Hawaii, but these are fixed, in that they cross the same way every day. The same exists on Europe to South America "tracks" and Hawaii to the Southern pacific and Australia. Theres are essentially the same as a standard airway, cross the same waypoints in the same space every day. At anytime you can usually do a random routing across an Oceanic sector just picking Lat/long coordinates or named waypoints as they best work for that flight that day, provided the random routing does not interfer with the prevailing track structures. I often have this when flying eastbound across the Atlantic during the active westbound NAT
When operating in these oceanic areas outside radar control and ground based nav aids, whether on a track or not, the aircraft must be equipped with some type of internal navigation system, such as GPS, INS, or for the olden days, a Sextant and star charts. I have no idea how much volume each region gets.
I think all the above is pretty close to accurate, let me know if I'm wrong... and i'll blame my training department.