No way! Anime can be made from all sorts of things. Sometimes they're the brainchild of the animation studio, sometimes they're based on games or other forms of literature. Manga is just one of the many starting points for anime.
No, not necessarily. Anime can be based on various sources. Some are inspired by novels, some by visual novels, and others are completely original concepts developed by the animation studios.
Not all anime are based exactly on the manga. Sometimes, there are changes made for various reasons like creative decisions or to fit the animation format better.
The Azumanga anime doesn't cover every aspect of the manga. Some storylines and details might be left out for various reasons like time constraints or creative decisions.
No, the Berserk anime doesn't cover all of the manga. It selectively adapts certain parts, and some crucial elements and developments from the manga are absent in the anime version.