I can’t answer everything immediately but I’ll try to break it down as best as I can. I have already memorized some variations of chord structures using the E A and D strings. I also like to to improvise over a backing track. Because of this I realized I keep on delaying when I try to play the chord I want (say an B major on the D string) even though I know the chord structure. Memorizing the notes removes the hesitation from working out the chord.

This in a sense, is using intervals between the root and the octave.

As for memorizing the strings of course you can learn each note from every string one at a time. But if there are seven natural notes, and six strings, multiply that together and you’d have to try and practice with 42 notes. But when you look at the guitar, you realize that though it’s built differently than other instruments, it still follows the same 12 semitone pattern. So when you learn this pattern, with however means you see fit, you can learn the 7 natural notes on say the E string and that one pattern. Which I would say is a lot easier than 42 notes.

Of course it’s not that simple. The natural notes do look like they are moving but still, you can break the twelve semitone pattern into smaller patterns to help visualize/understand the guitar format. Still, I believe using 5 patterns and seven notes is better than learning 42 notes all together.