Depends on the state, but Federal law does require you to be 21 or older to purchase a handgun. Ammunition can be sold without any background checks or ID checks in some states.

When I was 18, I bought a 9mm Carbine so for me it was rifle ammunition.

21 to purchase from a retail, I believe it's still 18 to purchase from an individual, making it even more backwards.

Is that really so backwards? Seems to me that a personal sale is a more intimate exchange and it might be expected that the seller vets the buyer a bit more carefully than your average retail transaction, thus justifying the lower age restriction.

This is correct in Texas. It's rooted in an issue in how the ATF defines weapons.

It's rooted in federalism. The federal government generally doesn't have the power to regulate transactions between individuals within a state. When it has assumed such powers, it has required some legal gymnastics.

A gun dealer with an FFL has a license to do interstate commerce in firearms and is subject to federal regulations on the subject. A private sale is governed by state law.

Not only automatic rifles. Hand grenades, fully-automatic grenade launchers, anti-tank rocket launchers, claymore mines... You name it. The infantry can be pretty fun.