How does a photon's wave energy propagate through free space?

[mfb]

(and indeed, i is mathematically undefined)

It has a well-defined mathematical description.

it would mean if I did something here on Earth it could instantaneously affect something at the other side of the universe. This is not what we experience in our day to day life - we don't see things around us is affected by things light years away instantaneously.

It would not change much if we ignore the effects on particle physics and cosmology. You would instantly be affected by the current locations of the stars in Alpha Centauri - so what? We are influenced by their positions approximately 4 years ago, but we do not care because that influence (and, in particular, its change over 4 years) is negligible.