Diablo – Do attacks that hit multiple enemies (or one enethe multiple times) generate multiple on-hit triggers

Yes, it is indeed possible.

Take a look at this video. The Demon Hunter's Chakram clearly hits the Skeletal Archer twice, before obliterating it.

Look like I was mistaken. Upon further investigation of the Leoric (he has a fairly large hitbox) fight, it looks like the Chakram only hits once per target.

Way of the Hundred Fists consists of 3 attacks, which appear to be 1 hit, 5 fast hits, than 1 hit again.

The 5 fast hits counts as one hit for any on-hit effect.

For example, if you have 0 spirit and use the full Way of the Hundred Fists combo, you will have 18 spirit since it gives you 6 spirit per attack.

I also tested this with on-hit effects by removing all equipment except a weapon with an amethyst in it (which steals life on hit), and found that during the course of a combo, I'd only heal 3 times.

As for your other question about the Hands of Lightning rune, it appears you are getting 3 extra attacks with no damage decrease per attack. I played around with it a bit, and although the damage per hit fluctuated a bit, it seemed to average the same per hit both with and without the rune.

The three attacks each seem to do 1/3 of 140% weapon damage each, so your 5-hit combo is around 9.3% weapon damage per hit, which results in an extra 3 hits giving you another 28% damage.