A firing pin is a movable pin in a firearm that strikes the primer of a cartridge to set off the charge. In the case of the AR-15, it is located in the bolt carrier group and can be easily exchanged in the event that it is damaged or ceases to function properly.
A flash hider is a device which attaches to the muzzle of a rifle that helps to reduce the amount of flash/light seen by the shooter while firing by cooling or dispersing the burning gases that exit the muzzle.
The main purpose of a flash hider is to lessen the flash that the shooter sees when the firearm is discharged. A common misconception is that it’s primary goal is to lessen the flash signature seen by the enemy when the gun is fired.
Flash suppressors are very different from muzzle brakes! While they are both located/mounted in the same place on the AR, muzzle brake is used to reduce the perceived recoil a shooter experiences (and typically has zero to do with eliminating flash), while the flash suppressor only limits the amount of flash the shooter sees and usually does not affect recoil.