However, It is not legal to ship firearms and ammo in the same package.
AND, it is not legal to ship firearms except from one FFL license holder to another FFL license holder.
I remember this from my younger days when I worked at UPS. Boxes fall apart sometimes...it couldn’t be helped. When a firearm was discovered(it happened more often than you would expect), it had to be turned over to management. Then they contacted the ATF or the FBI, I forget which. IF there were any violation, they sent an undercover agent to UPS and dressed him up in UPS uniform and sent him to the address in a UPS truck. Whoever signed for the package was arrested.
I believe that you are correct.
Except that "A person may ship a rifle or shotgun to himself, in care of a person who lives in another state, for purposes of hunting."
Not necessarily the case.
For example: "US Mail: An unlicensed person can ship a rifle or shotgun by US Mail." (from the following shipping summary from gunbroker.com) http://www.gunbroker.com/Support/SupportFAQView.asp?FAQID=1118&NoCount=1
And non-licensed people can even ship pistols for repair (usually, back to the manufacturer).
Not true. If you need to have a firearm that you own repaired, you can ship it directly to the manufacturer. The manufacturer can ship it directly back to your home address. You do need to sign for the package when it arrives. That's a good idea. Who wants UPS dropping a $400 to $1200 firearm off on the doorstep?