I like delicious food, I also like sports, such as badminton, basketball, etc. Like can also be replaced with love, enjoy, interested in. For example, such as can be used, or it can be replaced with like.

You can use etc, or you can change it to and so on.

There is no need to add verbs before food and sports. Regular English does not include eat/have food, play/doing sports, etc. It belongs to Chinglish.