How to resolve the warning on my homepage, after deleting mini panel?
It seems like your problem is caused by what is detailed in the issue about PHP 5.3.9 Strict Warning on Panels Empty Value. It was first reported in Panels 3.2, and has status 'Closed (Fixed)'.

The patch in comment # 15 of it should help you resolve the error. And according to comment # 26, this patch is included as of Panels 3.4.