What does a user need in order to:

2. Delete an Insightboard - the user, his/her team, his/her role or everyone in the account must be added to the Insightboard’s granular permissions with “delete” rights, also to perform these actions the user would require "Manage data" permissions on their user role.

3. Add insights to an insightboard - the user, his/her team, his/her role or everyone in the account must be added to Insightboard's permissions with the "Update" action. The user's role must also include "Manage data" and "Access Insightboards" (for example "admin", "data" roles, or a custom role with these permissions) permissions otherwise the user won't be allowed to view insights.

4. Modify permissions granted to an insightboard - the user, his/her team, his/her role or everyone in the account must be added to Insightboard's permissions with "Modify permissions" action.

Learn more:

How to set custom permissions on insightboards