Congratulations. (I'm not been sarcastic.) You've actually clearly stated the major commonsense assumptions that relativity violates.
If i'm travelling near the speed of light and fire a bullet from a gun i'm holding will the bullet slowly leave my gun because it can't possibly travel faster than the speed of light :)
No, because velocities in relativity don't add in that way as described above.
If stationary the speed of light is therefore c when moving light is potentially c + my speed is it not?.
No because a fundamental premise of relativity is that c is the same for every observer no matter how they are moving. This isn't just an assumption but an experimental result (look up the Michelson Morley experiment) that relativity explained. Also there is no such thing as 'stationary'. That's not strictly a result of relativity, but relativity's description of how relative velocity work pretty much put paid to any hope that the universe has some preferred velocity against which all others are measured.
because i'm nearly travelling at the speed of light whilst holding my gun would I be incapable of running around in my ficticious spaceship?
It follows from the last point that you're not really "travelling at the speed of light ". You maybe with respect to say the Earth, but if so it's equally true that the Earth is " nearly travelling at the speed of light " with respect to you. What matters is that if "nearly travelling at the speed of light " is say .999 c and your gun fires a bullet at say 0.002 c the velocity of the bullet with respect to the Earth is still going to be less than c. Counterintuitive, yes but the fact is space and time simply don't work in the way our commonsense tells us they do.