That article was a good read about the knife laws.
Very down to earth and sensible!
As for an axe, they can be as dangerous or in the wrong hands, more dangerous than a chainsaw..
The advice given on this thread by dandan is very good, very sensible and straight to the point. There is only one other thing I would add to that..
Raise any wood you want to cut off the ground, get yourself another piece of wood, cut a "V" shape out of it to lay your logs in so that you cut the raised end.. (I say wood because you can use it for the fire later if you want as well, and you can use it as a chopping block when you turn it over).
NEVER EVER cut any logs while they are laying on the ground. If the blade of the chainsaw hits the dirt and a small rock in there you can get kickback like you wouldn't believe and take your face off! (even if the brake works)
AND ALWAYS make sure your brake works. If it ever ceases to work take the chainsaw in for immediate repair!
While I'm not a logger, or sawmill worker etc, I was raised with chainsaws from a very young age, if I can give any sensible advice please drop me a PM.
But as already said, "if in doubt, don't"