Wilting is inevitable if you place basil in the refrigerator. This herb will also absorb smells from other foods surrounding it. Basil should be treated in the same manner we would treat a flower. Prepare a cup of fresh water and let your basil be outside of the cooler. However, freezing blanched basil is fine. This is recommended if you intend to store the herb for a longer period of time.
Ketchup can be kept outside of the refrigerator for years. The reason is the high content of acids that act as preservatives that won’t allow bacteria to grow and develop. Besides the acids absolutely all manufacturers add preservatives to maintain the quality of the product. Even after the jar was unsealed and used, it is still safe to keep it outside of the fridge.
Do not worry. Your cereal can be stored in your pantry or cupboard and there is no risk your favorite breakfast food will taste worse if not stored in cold temperature. Actually, low temperature as well as moisture can only make cereal taste worse and not as crunchy.