Good to know. Our area has periodic "cougar sightings", although I'm in the woods at least twice a day with my dog and have never seen one. The odd black bear, coyotes for sure, and deer often but a cougar, not yet. However, that could be the cougar's plan.
It is indeed. Any (big or small) cat prefers to stalk from behind and attack from behind. Running away from them creates an irresistible target. So if you encounter a mountain lion, you should face it and slowly back away. Loud noises are usually effective against any larger predator such as mountain lions or even bears, so yell loudly at it while you back away. The yelling alone may cause it to depart.
So if the cat has done its job right, you won't see (or hear) it until you've been knocked to the ground. It's not looking good for you at that point though.
Cougar sightings seem to be more common in borderline urban areas, where people see them on their property from inside their house. I'd call that the best way to sight a cougar. (unless you just put out the dog)