Is it possible to earn enough skulls to unlock everything in Orcs Must Die 2

I can't confirm this because I haven't played enough, but it seems like the scoring is pretty similar to OMD 1, so you might find this question useful. It links to a post on Robot Entertainments blog that has the point values for various combos and whatnot.

Aside from, getting high combo scores has been the best for points as far as I can tell. So combine a lot of different trap types with magic/attacks to get higher scores, each type of different damage source should increase your combo (ie, combo only increases once per type of trap that hits an enemy). I don't believe that coin forges actually help with your score, they just increase the amount of coins you have to spend during that level, so replace them with tar/fire traps to increase your combo multipliers.

According to a Robot Entertainment employee:

A little trinket design heads up.

Trinket passives apply to the owning player only while the active effect apply to both the owning and the coop player.

Example: The healing trinket only passively grants regeneration to the player that equips it but activating it will heal himself and their coop partner.

I did find a specific mention of the scavenger trinket having a unique property:

All Trinket Passives apply provided they are in your loadout, and only for you not your co-op partner. The only exception is Scavenger, So long as one of your traps added a combo point scavenger applies its passive effect even if the killing blow was dealt by your co-op partner.

All Trinket Active effects apply to both players.

Source: Robot Entertainment Forums

Source: Scavenger Trinket Passive