The explanation is exactly what the maths says - pick a different path, and you’ll walk a different distance. There’s nothing else to it.
No, I showed you that there’s no paradox that needs resolving. It seems to me that you’re wilfully refusing to “get” this.
There’s no such thing as “relative to waves”, because light has no rest frame. The speed is always between emitter and receiver.
Because it’s he who experiences acceleration locally in his frame. The equivalence principle tells us that uniform acceleration is locally equivalent to a uniform gravitational field; differently put, the accelerated twin sits at a different gravitational potential, which implies frequency shift.