My favorite food iscuisines are Korean food & Japan foodsese.

More natural sounding.

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.

Plural as two types of cooking.

My favorite food iss are Korean food & Japanese foods.

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

My favorite food is Korean food & Japanese foods.

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

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

My favorite food iss are Korean food & Japanese foods.

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

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

My fFavorite fFood

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

My favorite food is Korean food &and Japanese foods.

(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".

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