Diablo – How does “elemental” damage on weapons work with elemental skills

Companion damage scales based on attack speed. This was confirmed by Bashiok and tested by theorycrafters, who arrived at these numbers*:

APS    Companion Damage
1.00   30%
1.34   40%
1.40   42%
1.43   43%
1.60   48%
1.84   55%

*Calculated by looking at the in-game tool-tip, which changes based on the APS of the character.
Note: The wolf, being a shorter duration (25 seconds), does twice the %.

That is, the companion does the % of your weapon damage based on your APS. If it follows this logic of being a channeled DoT (which is what most theorycrafters have come to agree), then based on Bashiok's post, the tick rate (how often it attacks) increases as your APS increases. As for speed it attacks, it would behave like any other DoT in this situation. It would attack once per cycle for its inherent percentage, so if your APS is 1, it attacks once per second for 30% weapon damage. If your APS is 1.6, your cycle time decreases to 0.625 seconds per attack (1/1.6), so it would attack once every 0.625 seconds for 48% weapon damage. If it follows this model, your weapon damage would have nothing to do with companion damage, but its speed (and therefore indirectly, its dps) would affect companion damage.

As for the boar companion, it says on the wiki that it "strikes multiple enemies with every swing."

Edit: After some testing with a level 60 demon hunter, it appears that the percentages are roughly correct. For the ferrets, even though they are animated to attack separately, it seems the total damage is split between the two. The boar is really hard to judge, but as far as I can tell, the damage is the same as the others, just as a cleave attack that hits enemies in front of the boar for full damage to each.

All this information is gathered by personal experience or by experiences posted on Diablo forums that were confirmed by more than one person. It's difficult to get exact answers until everyone starts posting their findings, since Blizzard rarely explains how game mechanics work.

It depends on the skill in question.

First off, channeled skills are exactly the same as normal skills in terms of triggering things, except you do not need to re-cast the ability between each tick. Each channeled skill has a "Tick" (that occurs more often the faster attack speed you have), and it is these ticks that trigger on-hit effects. Each "Tick" is when you pay the resource cost of the skill.

Now, whether channeled skills are better depends on the on-hit effect you're trying to use. Anything with a listed % chance on hit, e.g. 1.1% chance to fear on hit, will be better the more attacks/ticks you make. Something listed as a "chance to happen", such as the wizard's "Critical Mass" i. e., "Critical Hits have a chance to reduce the cooldown of your spells by 1 second. " are most likely set up for ppm (proc per minute), which means you have a better chance of triggering them with a slow weapon, with the intent that you get the same number of triggerings, procs, over any given time period as a faster weapon.

Lastly, bear in mind that all that matters is the "Tick" times. If Rapid Fire shoots 10 arrows per Tick, all 10 of those arrows represent a single chance on hit (much like the Monk's Way of a Hundred Fists)

So to conclude, no, it is not better to use lots of channeled / DoT skills, for the simple reason that they don't provide any innate advantage. Unless you're fishing for Procs, you'll gain a much better chance to trigger things by using a faster weapon than any particular ability.