No, definitely not. Many anime are inspired by various sources. For example, some come from novels, while others are developed independently by animation studios with unique storylines.
Well, usually the anime might have some changes in pacing or added visual effects. But for big series, the core story and characters remain pretty similar.
In many cases, the main differences are in the visual style and pacing. The anime might have more dynamic animations but could rush or expand certain storylines compared to the manga.
Not really. Many popular series have anime that stay quite close to the manga. Minor differences might exist, but they usually don't change the core of the story.