Damage resistance applies to each strike.
So, you would take 1 damage from the first, and 3 from the second, for a total of 4.
The same is true if it's a claw/claw/bite/gore multi-attack, a two-weapon fighter, or a group of enemies.
If I have DR 5/- and an enemy level 6 Fighter makes a full attack against me, which outcome is correct:
He hits me for 6 damage on the BAB +6 attack and 8 on the BAB +1 attack.
Outcome 1: I take 6 - 5 + 8 - 5 = 4 damage total
OR
Outcome 2: I take 6 + 8 - 5 = 9 damage total
Whichever outcome is correct, does it apply similarly to 2WF?
Outcome 1: Each time a creature attacks you, the DR that the character has is applied to all the attacks that hit you. Per your example, if he hits you with his first attack for 6 damage, he only really dealt 1 (which is the minimum DR can reduce attacks to, as far as I know), and hits you with his second attack for 8 damage, he only really dealt 3.
When I state Each time, I also refer to Natural Attacks, Flurry of Blows Attacks, TWF Attacks, Swift Attacks, you name it.
However, feats such as Vital Strike and its upgrades are great for limiting/reducing the overall impact of DR. In addition, there are feats such as Penetrating Strike and its improved forms that reduce DR's effectiveness (down to 0).
which is the minimum DR can reduce attacks to, as far as I know
No, DR can entirely negate an attack, which also prevents you from being poisoned (and possibly other things).
Bobson's correct -- DR can completely eliminate damage.
Reduction vs Resistance--same thing?
Not the same thing, but it functions in a similar manner.
Energy Resistance applies to each source. (IE: Resist fire 5 would take 5 points of damage off each scorching ray. If there were three rays and each dealt 5 damage or less, no damage would be taken) If no damage is taken, then it won't interrupt a spell.
Energy Resistance does not have the same text as Damage Reduction, specifically "Whenever damage reduction completely negates the damage from an attack, it also negates most special effects that accompany the attack, such as injury poison, a monk's stunning, and injury-based disease."
Thus it can be assumed that a spell like Shout will still potentially deafen someone, even if the sonic damage is negated, and a creature affected by Elemental Touch (Cold) can still be fatigued even if it takes no cold damage.
The spell Resist Energy specifically mentions this, but the Glossary and Universal Monster Rules sections on resistance don't.