Does bonus damage against <Mob type> apply to elite mobs of the same type?

Yes, damage bonuses stack. In addition, different damage bonuses seem to be multiplicative while bonus damage of the same type is multiplicative additive. For example, if you have 1 piece with 50% bonus damage to elites and another with 50% bonus damage to elites, you would have 100% bonus damage to elites. If instead the second piece was 50% bonus damage to demons, then against demon elites you would do 1.5*1.5 = 2.25 of your normal damage, or you'd get 125% bonus damage.

Some of the different bonus damage types include damage to elites, damage to slowed mobs (dh passive I think), damage to chilled mobs (wizard passive), bonus damage (buff type spells, like Magic Weapon for wizards), damage to demons, and the affix that says something like "Cold skills do xx% more damage". The zuni boots affix is treated a little differently, as others have stated, but it is similar in that those type of affixes are added before determining the bonus damage, even if the affixes are different elemental types, like fire, arcane, cold, poison, etc. The only real difference is that it only applies to the physical damage you do, so weapons with +arcane damage or any other elemental type won't benefit from those affixes as much as one with just +min/max damage.