Borderlands – Will an item that gives ‘fire resistance’ lessen the damage that Krieg the Psycho gets from self-immolation

No, they don't.

What happens is if the shield is not hit with any other elemental damage (Slag, Corrosive, Fire, Shock or Explosive), it acts exactly like a normal shield and takes normal damage.

If you take damage from a rocket it is counted as normal - so be careful around rockets.

Also if you have health issues (and that's why you're using adaptive shields) try transfusion MIRV grenades - they are lifesavers.

Whenever you shoot an enemy with a shotgun, typically only one damage number pops up. So just because of just that I would assume that they take full damage from the shot.

On larger enemies however, if you are far away and the bullets are spread out enough it could pop up 2 or more numbers for damage depending on how large the shotgun's spread is and the distance the bullets traveled. Not sure if that will work the same in this case.