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What's the problem? 

If your FB page's profile picture is showing as a question mark in ManyChat, this signifies that you have age or country restriction set up for this Facebook page. 

How to troubleshoot?

If you don't need those restrictions and want your profile pic to show up properly in ManyChat, you can remove the restrictions here:

Note that the question mark instead of the profile pic is only visible to your ManyChat account admins and it doesn't affect your FB page or subscriber experience in any way, so you may as well choose to leave it as it is.