Can I grill a chicken/turkey breast in the night and eat it 12:00 and 18:00?
Any kind of cooked meat or fish and most perishable foods in general are safe as long as they are fully cooked and refrigerated within 2 hours (although the quality will deteriorate rapidly with fish).

If you plan to eat the leftovers twice then refrigerate two individual portions. Reheating the same item multiple times raises the risk of bacterial contamination. That is really the only thing you need to concern yourself with for short-term storage.

For more information see the USDA Basics for Handling Food Safely.