You can't delete individual messages, but if you want you can delete an entire chain of messages from a specific user. To do this, go to «Messages», and tick the box next to the person whose messages you want to delete. A yellow window will pop up with a list, saying «Move to the folder». Choose the «Ignored» folder, and click «Move». Afterwards you can clear the «Ignored» folder, by clicking the link next to the folder.
You cannot move system notifications and messages from the Support Team into the «Ignored» folder.
Search not available because you have deactivated «your profile participation in search». To remove limitations you must