Yes
no, but you can iron them.
No, only USPS can place mail in PO Boxes.
Yes, you can buy both moving and shipping boxes at the UPS Store. The UPS Store even carries cardboard "luggage" in case you have to carry more back on the plane that you expected to.
If you go to the UPS Store they can sell you boxes. They also have foam to protect your items.
Yes, USPS does but UPS and FedEx do not.
Shipping boxes.
Freight would be the best way, if you have a lot of boxes. You won't have to worry about some boxes not showing up, if they are strapped on to the pallet. For a few boxes you can send them FEDEX ground or UPS ground.
you can buy basic sized mailing boxes at retailers. some to check at the UPS store and office stores.
Check out BoxGiver. There’s a bunch of free moving boxes on there
There is a gold mine of used boxes usually behind any store, but specifically for clean boxes you can go to UPS stores. A good option in Dallas is "Tree Hugger Boxes", where you can pick up boxes and then later drop them back off in good condition .
UPS does offer free boxes for shipping. You can go on the UPS website and order what you want and they will bring them right to your door.
The UPS Store, U-Haul, and The Moving Store sells cardboard moving boxes. Big box stores such as Staples and Walmart also sell cardboard moving boxes.