I'm not a pianist, but I can try and help out with the theory/analyzation as much as I can.
1. I would personally start with analyzing all the rhythmic motives, and then move onto analyzing the harmonic motives. In terms of analyzing the harmony, just from glancing at the bass there's already a ton of information I could pull from it (chord changes, modulation). The rest is really simple, I'm not sure how much you want to dig into the piece, but it shouldn't be too difficult.
2. You're right, it's just a tonic run, over G Major.
3. Can't help you all that much with this one, since I'm not a pianist, but again, I would start with the rhythmic motives.