If the lock is at half or full cock, is there any chance that the hammer could be released to fire the gun? Say, if a branch hit it or I dropped the gun. Or am I being too paranoid?
You can test the half-cock notch yourself, at home. Just make sure you have a flint (or wooden "flint") in the cock (to keep from damaging your lock), and the frizzen closed, before you start trying to make the half-cock notch fail on you. And I sure wouldn't suggest you hammer on the cock itself; that'd be an excellent way to break it.
With your lock in full-cocked position, yes: it'd be pretty easy to find a way to accidentally trip the trigger and fire the piece. That's why you NEVER go to "full-cocked" position, and definitely never set your triggers, until you're ready to destroy whatever's in front of the muzzle.
I'd suggest you pull your lock out of the mortise, and watch how the whole guts work: should be pretty easy to see what we're all saying, that way.