Is wearing a flag patch on a backpack against regulations?

Yes

YES

Not in my opinion.

Regulation seems ambiguous! Could go either way. Depending on where you take a breath!

Horizontal. Highest of insignia and touching no other objects.

Display properly

I don't know about the regulations but when I was in the Army, no embellishments of Army issued equipment would be permitted.

I was trained that it was, until OEF/IEF

Yes

As far as know that is up to interpretation as you are not to alter, change or disfigure any military issued equipment. Adding a patch of any kind could be considered an alteration.