No. Weapons or ammunition of any kind may not be transported via consumer air travel.
Not true. Weapons or ammunition cannot be in Carry-on luggage. Weapons and Ammo can be in checked baggage as long as you declare it , and meet the TSA and airline guidelines. Folks, READ the question, please. The "Empty ammo can" may be brought on. However, there may be residual residue which WILL cause much concern. (The white fabric disks they rub on carry-on is testing for explosive residue and will test positive, whch will take you out of line for further examination, personal body search and detail examination of your luggage, including checked bags.) Most un-wise.
Assuming you mean a rifle such as the SMLE, the cartridge used in the .303 Enfield, also called .303 British. See the link below for information on this ammo. However, if you are not certain (some military surplus rifles were rebarreled into other calibers) have a gunsmith take a look at it.
.410 ammo
Take it to a gunsmith.
Any standard .380 ACP ammo, yes.
You have a ball on an airplane..
The link at the bottom of this page will take you to a good site on military surplus firearms, including assembly and disassembly of the Mauser rifle. Your bolt MAY need to be cocked.
Lincoln's Repeater uses .44 Magnum ammo.
Depends on the kind of airplane.
no
no
No.
9mm rounds.