Can keys drop from zombies?
Solution 1:
They are dropped. The time between drops seemed random and sometimes too long IMO, but i got keys for every gate except for the ones in the 3rd world (still playing...)
Solution 2:
From the official Support page (click on "Stars, Keys and the Gates they Open!"):
If you don't have enough Keys to unlock a gate, you can replay levels to earn more. Keys may appear in any level or mini-game, as they are dropped at random by zombies. Keys also may be among the treasures found in Yeti Zombie Lunchboxes.