WASD or Arrows for movement.
Z or Keypad 1 for your gun. (Check numlock)
The reason the mods do not cost money to unlock, is that they have different weaknesses and strengths. Some of the mods can't hit short enemies and some have a bigger bullet but are slower to fire, etc. They're mods for your basic gun. Not new guns.
There is no penalty for death in this game. You don't lose money, you just have to retry the map, possibly change your weapon mod. Different mods work better for different levels.