Secondly; do they "pierce"? Do staff attacks benefit from skills like Hungry Stalactite?

If you hover over the default staff attack on your skill bar you can get a full stats list similar to what you get from spells in the spell menu. Notice that staffs have "Pierce Strength: 1 Targets"and the tag "Projectile"

Functionally, I can verify that they benefit from projectile perks. I'm using a staff and I'm benefiting from Archion's Teachings currently (+1 projectile to projectile skills). The projectiles both go the same place on a staff so it's hard to tell, but the projectile got brighter from the overlayed projectile, and the staff stats (as mentioned above) show 2 projectiles instead of 1.

I have not functionally tested benefiting from pierce skills like Hungry Stalactite.

I hope that helps!

Interesting, I was just wondering about Archion's Teachings with a mage staff. Unfortunately, it does not appear to increase my willpower regeneration.

I tested the effect of pierce and bounce passive skills with the basic staff attacks.

Pierce works, albeit inconsistently. Sometimes it will stop at the target. Other times it will go through the target, and bounce to other targets, effectively hitting four times.

Bounce is much more consistent. The passive skill that gives basic attack projectiles two bounces, actually adds two additional bounces to the staff attack. The perk after that adds another one. So if you invest in that line, your basic attacks will hit six targets. Add another projectile and you have a total of twelve hits.

This is NOT the case in my game. When I hover the mouse over my staff it says it's a two handed weapon how much willpower is generated per attack and what damage it does. Nothing about if the attack is projectile or spell.