You can create several sources and event filters in Engage Inboxes, to help gather all of your incoming messages and comments in one place.
Mentions in a comment on any post.
Mentions in a caption on any post.
Comments on your own posts.
For Instagram, you're also able to collect tickets based on historical data.
Messages from your messenger conversations.
Comments on posts on your page feed.
When a person reaches out to you through Messenger you have 24 hours to respond. If the person does not send a new message after the 24 hours are up no more messages can be sent back. This is due to Facebook policy.