Answer the direct messages your Instagram account receives.
Instagram is usually reached through the Page it is linked to, so connecting starts with the Page even though the conversations are on Instagram.
One signup connects the Page for Messenger and the Instagram account together. They stay separate here, so you can deploy this flow to Instagram and a different one to Messenger, or deploy to only one.
If the Page has no Instagram account linked to it, the connection will say so rather than appear empty. Link the account at Meta and connect again.
A professional account that is not linked to a Page can be connected on its own. The option is under the account list, and it takes you to Instagram to authorise rather than opening a window, because Meta serves that sign in from Instagram itself.
Use it only when there really is no Page. An account connected through its Page keeps things this route cannot do, including ads that open a conversation and conversation tagging, so linking a Page is the better answer whenever it is available.
People reply to stories and mention you in theirs, and both arrive as direct messages. Neither is answered until you ask for it, so the bot stays quiet on both until you switch them on in the deployment's Instagram settings.
Someone replying to a story you posted is starting a conversation with you, so this is the one most accounts want on. Off by default all the same.
Being tagged in a story is often not a message at all, and a busy account can be mentioned constantly. Leave it off unless you want the bot to answer every one of them, and remember that each answered mention is a conversation.
Off means nothing happens at all
While one of these is off, that kind of message is not answered, does not appear in your inbox, and is not counted. Switch it on and it behaves like any other message.
Instagram follows the same limits Messenger does.
For 24 hours after a customer's last message, anything can be sent freely. Almost every conversation happens here and you will not notice a limit.
After 24 hours the bot stops replying and only a person may answer. The inbox says so when an agent is in that window, because Meta allows it on the understanding that a human wrote it. Keep it a personal answer rather than marketing: sending a campaign this way is a policy violation, and it is your account that carries the consequence.
Nothing can be sent, and the inbox will stop you rather than let a reply fail silently. Internal notes still work.
Comments on your posts are a different thing from direct messages and are not answered here.