How does Pix's damage work?

Solution 1:

Here are the answers to this question(s) one-by-one:

What does [Pix's] damage scale from?

Pix's damage scales with Lulu's level. The formula for Pix's damage is:

Pix fires a barrage of 3 bolts, dealing 3 + (2 × level) magic damage each

Does it scale with AD, AP, etc.?

As you can see from the formula above. it does not scale with Attack damage (AD), Ability Powers (AP) or any other champion stat (Mana, Health, etc.) and is based solely on Lulu's level.

Is Pix's damage Magical or Physical?

Pix deals magic damage exclusively. Therefore his damage is dependent on the users Magic Penetration and the targets Magic Resist stats. There is some speculation about whose Magic Penetration Pix uses when making his attacks from an ally (not Lulu) as noted in this link.

Does Pix attack when the ally uses spells, or just for autoattacks?

Pix's attack is triggered by autoattacks only. Casting spells that refresh the attack animation (Nasus's Siphoning Strike, Blitz's Power Fist, etc) may provide additional attacks from Pix but to maximize the damage you probably want to target a champion with a higher attack speed.

For more information about Lulu and Pix check out her entry on the LoL Wikia.

Solution 2:

According to the LoL Wikia,

Pix, Faerie Companion deals Magic damage, and scales with Level rather than items.

Pix fires a barrage of 3 bolts, dealing 3 + (2 × level) magic damage each, at whomever Lulu attacks. These bolts are homing but can be blocked by other units.

Solution 3:

Pix's damage does not scale with ap or ad, but rather with level and attack speed:

(Innate): Pix fires a barrage of 3 bolts, dealing 3 + (2 × level) magic damage each, at whomever Lulu attacks. These bolts are homing but can be blocked by other units.

Source