I am really like this food but how to cook I don't know ithow to cook. I really like this food but I don't know how to cook.

Here, you can actually say "I really like these foods". You can use "foods" here, because unlike in the previous sentence, it now refers to BOTH Korean and Japanese food. Of course, your original sentence is still perfectly okay.

I am really like thisese foods but how to cook I don't know ithow to cook them. I am really like these foods but I don't know how to cook them.

I am really like this food but how to cook I don't know item but don't know how to make them. I really like them but don't know how to make them.

I am really like thisese foods, but how to cook I don't know ithow to cook them. I really like these foods, but I don't know how to cook them.

I am really like this food but how to cook I don't know itese types of food but have no idea how to cook them. I really like these types of food but have no idea how to cook them.

Plural as two types of cooking.

My fFavorite fFood My Favorite Food

It's a minor issue, but it might be good to follow title capitalisation rules.

My favorite food is Korean food &and Japanese foods. My favorite food is Korean and Japanese food.

(1) You can combine "Korean food" and "Japanese food" into "Korean and Japanese food", to avoid unnecessary repetition of the word "food". (2) Your use of the ampersand ("&") is correct, but in most scenarios, especially when writing somewhat formally, we'd just write out "and" in full. (3) "Food" is generally an uncountable noun. "Foods" refers to different types of food, like food from different cultures, such as in the sentence "I've eaten foods from around the world." However, here, since "food" refers only to Korean or Japanese food, we don't use "foods".

My favorite food iss are Korean food & Japanese foods. My favorite foods are Korean & Japanese food.

"Foods are" since you reference two types of food.

My favorite food is Korean food & Japanese foods. My favorite food is Korean & Japanese food.

Alternatives: I like Korean and Japanese food. I like Korean and Japanese cuisine.

My favorite food iss are Korean food & Japanese foods. My favorite foods are Korean & Japanese foods.

My favorite food iscuisines are Korean food & Japan foodsese. My favorite cuisines are Korean & Japanese.

More natural sounding.