2. You can remove one them, right click on it, remove.
3. NOT A BUG: I don't know why are you expecting the service process of an anti-virus that has to be ready to scan files as they are accessed to enable app nap? App Nap is not only related to apps not being visible, and avast helper is actually a service, that has no visible front-end. The Avast window, when it's open, is another process, also, as a service it should always be in a running state, app nap only applies to apps that can be frozen, finally, the developer can decide if they allow OS X to apply App Nap or not, again, and again an Anti-Virus should not be frozen.
4. NOT A BUG: This is actually intended, although I don't agree with it.