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.
It's in addition to his AD. Similar to and item like Wit's End, you'll see two numbers when you hit someone (100 + 10 = 110, in your example)
Best Answer
The Recharging starts roughly 0.5 seconds after your last triggering of the passive and it takes 10 seconds to reach its full damage. This charging time cannot be reduced by any stat.
Every hit will deal your amount of souls as bonus damage (regardless of charge time).
After 5 seconds you will deal half the bonus damage you'd deal at max charge + your souls and after 10 seconds you will deal the bonus damage that's displayed on the tooltip.
Note that Attacks against structures and wards will not reset your counter since it's not triggering the passive.
The bonus damage scales off your Total AD and your collected souls and it's a magic-damage on-hit effect which means that it will not benefit from spellvamp or lifesteal.