The area is also patrolled by the park rangers and environmental police.
I've hiked with my children and never run in to anyone on anything but a bike, but even so any motorized vehicle you'd hear coming from a mile away, as it's a very quiet forest. I think it's perfectly safe as long as you are aware of your surroundings and wear bright colors or have a friend if you're hearing impaired.
No, for the most part it will be very rare to run into someone on the paths, and even more rare to meet someone driving through the forest. Some of the paths are very steep and dilapidated, so even if you do find someone they probably wont be driving too fast.
Thanks! Your answer is awaiting moderation.