Is wearing a flag patch on a backpack against regulations?

yes

If the army issues it ,then yes.

Easy answer. The CSM doesn't want you putting the flag patch on a backpack. It doesn't matter what you feel is right. Don't put the damn flag patch on a backpack. You're a PFC. You need to be seen and not heard, both by a preference of everyone higher ranked than you and as a suggestion from me to you so you won't draw unwanted attention to yourself.

Be small. Be unheard. Don't rock the boat, private. This isn't a fight worth the attention.

No

Yes

Yes. It is only allowed on the sleeve.

yes

Whether it is according to regulations or not, it certainly has been a common practice since at least the VietNam war. And has helped troop moral

No, if you are activated and heading overseas.

Yes