Yea, you could add those with After Effects. It has a particle engine (along with lots of other capabilities) and 3rd party plug-ins like DigiEffects Delirium have additional smoke and fog and a muzzle flash FX. There is also WonderTouch particleIllusion which is another excellent particle engine that costs less than After Effects but only does particles. FXHome makes EffectsLab Pro which will do everything you need as well. It was pretty much designed to do just what you need. I would download the trial versions of each or watch some tutorial videos to see how much of a learning investment you are willing to make.

There are also several effects stock footage libraries that have muzzle flashes and explosions already generated and rendered with an alpha channel. This is the quickest way to add FX if you don't want to learn new software.

~jr