He apparently shows up in the Bhavishya Purana, so questions about his role in that text would be on-topic. Questions about his place in the historical record ought to be off-topic.
Definitely not. Other than being Hindus, they have nothing to do with Hinduism whatsoever. Questions about him go to History.SE.
I can see questions about his religious literature maybe being on-topic, particularly in the context of a comparison with the scriptures (e.g. why does Kalidasa's Recognition of Shakuntala differ from the Mahabharata in aspect X). Questions about Kalidasa's non-religious literature and about Kalidasa himself should be off-topic.
Tulsidas's Ramcharitmanas is definitely on-topic. His other religious literature may also be (cf. what I wrote for Kalidas). Again, non-religious literature and questions about Tulsidas himself are probably off-topic.
Think about the implications of what you're saying. Should we just give carte blanche for any question about people who are Hindu? That broadens the scope of this site to an unmanageable degree.