"I have managed to pull off only two topics." Is this phrase correct? As manage and pull-off has the same meaning.
The two verbs do overlap.
To "pull something off" means to succeed in doing it; the phrase is often used in situations where the expectation was failure, not success, or where the task, when thought about, seems more daunting in retrospect than it did to begin with.
To "manage to do something" means to do it, perhaps accidentally, perhaps in a clumsy way, perhaps in a manner which could not be repeated again at will. The person who accomplished the thing has no mastery of it.