Yes. The Meta API requires a Professional Instagram account linked to a Facebook Page. Linking takes a minute in Instagram settings.
Yes. Comments under promoted posts and Reels arrive in the same inbox and follow the same rules as organic comments.
No. SMSBAT uses the official Instagram Messaging API from Meta, the same one used by Meta Business Suite. There are no unofficial clients or password sharing.
Yes, within Meta rules: a private reply can be sent to the author of a comment on your post, and the conversation then continues in Direct.
It says so honestly, offers to connect an agent and moves the dialogue to the team queue with a summary and the full history.