The main difference between road and trail shoes is the sole, trail shoes have a grippier sole for the uneven terrain, whilst road shoes have a soft flat surface.
Several trail shoes can be used for dual purpose, both the road and trail. The Hoka Challenger is ideal for both the road and trail.
No trail runners do not need to be waterproof, as they drain quite easily when going through creeks. Waterproof trail-running shoes would trap water inside and cause your feet sweat and go wrinkly, which is why many trail runners choose very breathable, non-waterproof shoes as an alternative.
Absolutely trail runners are ideal for hiking with their grippy soles and flexible design makes it easier to more about it on the trails. Hiking shoes will however provide more durability than a trail running shoe.