Definitely not. Batman is one of the most iconic characters from DC Comics. Marvel Comics has its own distinct set of heroes and villains that are separate from Batman and the DC universe. DC and Marvel are two different comic book universes with their own characters and storylines.
They could have a mentor - mentee relationship. Batman, with his vast experience, could mentor Captain Marvel on things like stealth and detective work, which are Batman's specialties.
No way. Batman is strictly a DC Comics creation. DC has its own distinct roster of heroes and villains, and Batman is one of its most famous and enduring characters, with a rich history and multiple storylines that are unique to the DC universe.