We're dealing with something so complicated that anything but an analytical mind is at a disadvantage. I'm scheduling 4 recitals this month coming up, 90 pages of music about, my most effective time spent is score studying. The fingers learn fast, the mind has to keep up.
My point is, it's necessary to deconstruct like this, because that's the essence of understanding. If you don't understand what you're doing, how can you communicate it clearly for an audience that's willing to give their time and listen.
As for the Sonata, I played it..... wow, 20 years ago when I was young useless dolt? And this sonata is quite far from outside of the box, and the development is highly standard developing theme 2 until it grows into basic motives and plays around with those until the birdie from the rocket theme prepares the recap.
As for what to call that theme, it's in a flat minor when it first appears so you can put it together with the A flat major theme after, all as theme group 2. This exact formula happens in the pathetique sonata (here it's defiant, there it's dominant is the main difference), obviously with an interesting development.
I don't think you need pencil and paper, but you need a lot of time to go through a great deal of repertoire, sight reading will develop, understanding and experience will grow as well etc etc. But it takes time.