The green you are seeing is probably moss or algae or both. Here's a couple of helpful sites.
The flat barnacle looking things are lichens. They are harmless to your roof and don't do any damage. They may just look unsightly. They are actually beneficial to wildlife.
When weeding, the best way to make sure you are removing a weed and not a valuable plant is to pull on it. If it comes out of the ground easily, it is a valuable plant.