No, Binary isn't a mutant. Her powers and story don't fit the typical mutant framework within Marvel Comics. Instead, they have a distinct and separate origin and development.
Captain Marvel is Carol Danvers. She gained her powers through an interaction with alien technology and has become a powerful hero in the Marvel universe.
I don't think so. The concept of 'strongest' is relative in the Marvel universe. Different heroes have their unique powers and moments of greatness, so it's not a straightforward answer to say Captain Marvel is the strongest.
Yes, Captain Marvel is definitely a significant character in Marvel Comics. She has her own storylines and plays an important role in the Marvel universe.