Nope, you don't need a rooster. But hens depend on roosters for more than just reproduction. Personally I wouldn't be without one. They are your first line of defense against predators. They tell the hens whether the threat is from the air or from the ground. They find food and call the hens to it. They herd the flock to safety whenever they perceive danger. They even build nests for the girls to lay eggs in then guard the girls as they are laying. Roosters are important to the dynamics of a successful flock.
If you are in a position to have chickens and are able to keep a rooster then by all means do. You will have a much happier and better adjusted flock. But most towns that allow chickens do not allow roosters. Yep...they noisy. After a while you don't really hear them but your neighbor might...
Predators are not a bad thing. Chickens only lay eggs reliably for about three years. After that they just become freeloaders. So the goal is to achieve a balance. Let them free range enough so that the predators pick off any extra roosters you might acquire and the older, slower hens.
Dogs and chickens have co-existed since time out of mind. Unless you've got a pack of wild unmanageable dogs they will get along fine. I had to whack my dog one time when he was young for chasing chickens. It's one of those barnyard rules that dogs are born with, sometimes they just have to be reminded.
Dogs are supposed to guard livestock. Not eat it.
**edit** also roosters should not be allowed to bully the dogs!