There is no delete all messages button, I'm afraid. To delete a status update, you will need to click the status update and view it. You can do this by clicking the status update in the block or going to the profile of the user who posted it. You can then delete it by clicking "Options" then "Delete" as outlined below in the screenshot.
Moderator permissions control what you can moderate on the front-end of your community, such as here. You will need to ensure your group has correct moderator permissions. Administrator permissions control what you can do in the Admin Control Panel so simply because you have an administrator account does not mean you have moderator permissions. For more on this, you can read the following Guide: https://invisioncommunity.com/4guides/staff-and-moderation/creating-administrators-and-moderators-r31/