His nose will get blacker with time. Most bulldogs noses turn completely black, but ours still has a pink spot even after 2 1/2 years. He should keep some of the spots around his nose, though, but no guarantees!
Good heavens he is a cutie! That puppy energy can be hard to handle and hard to redirect. He will go through phases, but if you want to keep him as a part of your family there isn't anything that the people here can't help you get through.