This is an attempt to solve the twin paradox via two Minkowski diagrams with a few questions attached. Note that there might be mistakes in this drawing i will fix in the course of this thread in case someone notices any.
First, let me explain the two Minkowski diagrams in the drawing first.
Blue Lines: a huge blue ruler measuring 2 light-seconds in length which is at rest within system A (inertial reference system in which Bob is at rest in at all times)
Purple Lines : a huge purple ruler measuring 2 light-seconds in system A which travels at vrel = 0.5c relative to system A. The purple ruler measures ~2.3 light-seconds in system B (inertial reference system the purple ruler is at rest in at all times )
Green/Light Blue Lines: back/front sides of a rocket with Alice residing at the back of the rocket. The rocket is at rest primarily in system A, and accelerates instantaneously to vrel = 0.5c, system B becoming it's new rest frame.
Yellow Lines: Those are light-beams traveling at C always, seen from within any arbitrary inertial reference frame. The x/t diagram is to be imagined in a way that ensures those light-beams having a 45° gradient.