Fair enough. If you want to call it that, that is fine, too.

Either way, she isn't rolling break away.

Adjacency and movement are two different concepts, aren't they?

I mean, of course they are different things, but isn't it easier just to say that she ignores the wall for movement purposes, but she does not ignore the wall for adjacency purposes?

Flyers ignore the effects of elevated terrain on movement. They don't need to break away from other characters at a different elevation in a square next to them.

Could Moonstone use her trait to charge an opposing character on the opposite of blocking terrain?

Yes. That is basically the point of the power.

I am totally failing to understand the use of this power anyways? She already has flight and thus can go over the Blocking if it is outdoors right? Is the only real application of her power for instances where a) she gets her flight countered or b) when she is indoors and cannot fly over the walls/blocking?

After reading her white power I immediately questioned all moves I've done so far with leap/climb and flight and now I've become confused.

It lets her Move/Charge through Walls/Blocking Terrain. Very useful Indoors, not so much Outdoors. Like some powers *coughHoTCapcough*, it's great in some types of maps and just "meh" on others.