How to fix persistant cracks on this section of the wall and why do they show up even after repainting?
Your 1st picture shows an issue where you have a layer of paint which is not well adhered to the surface underneath (and probably more layers painted on top of that).
This is like putting a piece of scotch-tape onto a dusty surface and expecting it to stick.
More and more layers of paint will never fix this.
You'd need to strip/scrape/peel all of the old paint off until you get back down to something solid and start the paint journey over again from scratch.  

While doing this you'll probably also find what's under that crack in the 2nd picture - there's likely still movement on each side of the crack, but it might be possible to manage this once you know what's under there...