From this guide:
Pack Alpha is quite an interesting Perk, particularly for melee builds as it gives you a 25% bonus to melee and unarmed damage. However, its secondary function is to provide increased damage resistance. This is not a flat amount, it actually takes incoming damage from energy/physical effects and reduces it by 25%. On top of your armor, this can be a huge bonus and may interest even non-melee players. Only problem is having to buddy up to The Pack!
Thus, it looks like incoming damage is just reduced by a quarter before it is applied.
As for how it stacks with Lone Wanderer 2 or Attack Dog 4, I believe the perks will stack with Pack Alpha, simply based on the way other perks stack on top of each other.
As to if it the bonus is active while using your fists, technically, yes, according to the description you posted:
Your damage resistance is greatly increased (25% less damage) and you deal more damage (25%) while unarmed or using melee weapons.
However, going back to the other guide, see this sentence:
On top of your armor, this can be a huge bonus and may interest even non-melee players.
Thus, the damage resistance is applied regardless of what weapon you are using (if any at all).