Is it possible to use facebook chatbot & normal(direct) messaging option in the same facebook page? That is, if i am available online, then can i directly reply to the user instead of chatbot. If i'm logged out, then bot must reply. Or is there an option to select by the user to message directly to me or chat with the bot?
Facebook is working on their "Handover" protocol and its currently in beta phase. Handover protocol will allow switching between bot and user messaging on same channel (chat).
More information in official documentation here.