Yes, Jericho will have infinite ammo but ONLY for the weapon he has when you recruit him. If you give him a different weapon, you will have to give him ammo regularly.

Yes, he will leave if you go from Bad Karma to anything else. This applies for all followers except for Clover, Dogmeat, and Charon.

The Terrible Shotgun can be found in Evergreen Mills. Head west from Megaton and you should find it. Inside the large factory, there should be a cave complex. Wander around until you find a non-hostile Raider named Smilin' Jack. He will have the shotgun on him. BE CAREFUL! There are over 30 Raiders in or around the area along with a Super Mutant Behemoth in a cage.

Lincoln's Repeater is located in the Museum of American History in D.C. itself. It will be in a display case. I can't really give better directions than that. NOTE: Lincoln's Repeater is repaired by Hunting Rifles. This includes Ol' Painless. Be very careful or you could lose it.

Ol' Painless is in the Republic of Dave in the far north-east corner of the map. Inside the main building, there will be a man named Dave. Either kill him for the key to his safe or rig the election so he loses. Either way, you get the key and the safe is in his office.

The easiest Fatman to find is outside of GNR. Follow the main quest until you get there. It, along with 8 Mini-Nukes, will be on a dead Brother of Steel on one of the benches.

I hope that my reply helps. If you need anything else, just ask.