If you right click on a component and "Change axes", you will modify the component axes only - the world axes will remain in their original position.
Right click (carefully) on any of the three world axes to place them elsewhere (if I correctly understand your problem).
Hidden geometry is under the View menu. It will reveal any hidden edges and faces as well as softened/smooth edges (like those of a cylinder or sphere for instance). This can be handy if you want to position some texture on them as you cannot access the position texture tools on curved surfaces but you can on the revealed facets when HG is on.