There’s a halacha that when showering one should start from the head down, when putting on clothes right side first. Is there any reason to do this with food to for example only opening a banana from the top first?
No, there is no reason to do this with regard to food.
The concept of placing right before left applies only to the person himself: We get dressed right side first, we hold items in the right hand when we make a berachah, we turn to the right (in hagbahah, korbanos, etc.), and so on. Outside the person himself, the principle does not apply.