How does the orientation of stars axes of rotation and any planetary systems relate to the plane of the galaxy? Is there any relationship that has been detected, are they grouped from their parental nebulae. Do galactic magnetic fields have coherent orientations that would affect nebula growth and consequent stellar growth.
No. there's in no relation as far as we know. Ecliptic plane orientations of other planetary systems with respect to the galactic plane are completely random as far as we know.
We know this also because we can find exoplanets by the transit method nearly in any direction of the sky; if we look at $N$ stars located at galactic latitude of (let's say) $20^\circ$ (thus their ecliptic plane has relative inclinations of $20^\circ$ with respect to the galactic plane) we find roughly the same number of transit events as if we look to $N$ stars at $0^\circ$ latitude (thus their ecliptic planes have relative inclinations of $0^\circ$ with respect to the galactic plane). Since we are probably not the center of a planetary conspiracy on which everything is aligned so that we see the same distribution in all the sky we can assume that inclinations are random and we just happen to detect a similar fraction of transits everywhere because we are looking at at the same fraction of the same random population in each direction.
Humanity has just started to observe other planetary systems so this might change a little but in principle if there is any "preferential orientation", for now, with our current knowledge it is completely camouflaged by the main random component of this distribution.