To add rules, go to ACP > Members > Achievements > Rules.
Click on the "Create New" button. You can define the condition in which to award rules. People that match the criteria going forward will receive the badge automatically. If you want people who already match the condition to be awarded the badge, you will need to rebuild your achievements.
Regarding deleting a badge, for badges that are awarded via rule there is no way that I'm aware of that will let you manually remove it from one person. You would have to remove the badge from everyone.