- Yes, history of philosophy is on topic per the help center.
- That is totally unanswerable and should be closed anywhere.
- I don't know a logical symbol of existence. Do you mean the existential quantification ∃? In that case, that would be borderline but I think I would not vote to close it, provided that the irrelevant second half of your question would be left out.
From the link above:
We welcome questions involving subjects like:
epistemology — the nature of knowledge and learning
ethics — the nature of the right thing to do
metaphysics — the nature of being and reality
logic — the nature of reasoning and inference
aesthetics — the nature of feelings and artistic sentiment
history of philosophy — the domains and personalities in the past associated with philosophy
applied philosophy — the more specific disciplines where philosophical methods are applied, such as logic and argumentation, the philosophy of language, political and social philosophy, psychoanalysis, theology, economics, the philosophy of science and mathematics, etc.