When do keys drop in plants vs zombies 2

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...)

From my game play observations:

While each bloomerang can hit a target twice (when going forward and then backward), those two hits combined, deal about the same amount of damage as a single pea from Peashooters. Thus, each boomerang can be considered equivalent to one pea, but can hit up to 3 targets - so equivalent to 3 peas if you have 3 or more zombies in one lane.

Plant Food:

When overcharged with Plant Food, Peashooters shoot approximately 20 peas a second for 3 seconds, that is 60 peas in one direction.

Bloomerang shoots approximately 10 boomerangs in all 4 directions when overcharged. That is equivalent to 10 to 30 peas shot to EACH direction when you have 1 to 3 targets.

In conclusion:

Peashooter: 60 peas in one direction.

Bloomerang: up to 30 peas-equivalent in one direction (if you have 3 or more zombies), theoretical max is 120 peas-equivalent in all four directions.

So without considering other situations such as grave stones in the way, or a really tough zombie in front protecting annoying zombies, it seems like you should feed a Peashooter for its maximum fire power.