Gallons shop is unlocked. Go to episode 2 shop on multiplayer mode.
To unlock the single player missions, you must unlock the appropriate government missions. So for the cave missions, you must unlock government mission 2-1. You can access those missions by going to the principal's area and speaking with Momoka on episode 1 and 4 and Nol on episode 2. These are done in multiplayer mode. Also, difficulty doesn't matter, except for the prizes you receive for beating the boss missions. So, if you unlock the government missions or the single player missions, they are unlocked on all difficulty levels.