Some things that should be written in foreign languages are items. There is no reason to change okonomiyaki into Japanese Pizza, Crepes, or Pancakes since even though it is sometimes considered to be those, it is not those. Sure some people may not know what okonomiyaki are but they should be able to figure out it is a type of food from how it is used.
If a character is Japanese give the character a Japanese name if you don't then at least explain why. This is just common sense. Japanese people will have Japanese names, English people will have English names, Spanish people will have Spanish names, etc. Sure occasionally an English person will have a Russian name but this is not very common and is usually remarked upon by others.
Attack names are ok to be in Japanese because even though it is not required or really needed they sound cooler. Example: Shishi Höködan sounds cooler than lion roar shot. (You could also just say he threw a ki blast).
I have seen people make this mistake before: they have a Japanese character introduce himself in Japanese to another Japanese character. On the surface this doesn't seem like a mistake. They are Japanese so it makes sense that they do so in Japanese. The reason this is a mistake is because the supposed setting is in Japan and we are to believe that everyone is speaking Japanese the entire time.
While technically there is nothing wrong with the following, it reads awkwardly. Japanese people will occasionally use English words while speaking. For instance the person may say "I'm Sorry" in English. To convey that the person is speaking another language some people will have the person speak Japanese and say "Gomen" instead of having it in English. This can be confusing for some people especially if you are purposely putting in Japanese words/phrases elsewhere in the fic to convey terms that don't translate well into English. In this case it is generally better to choose a third language such as Spanish and have the person say "lo siento" or convey it by other means.
Foreigners in the fic should use their native tongue occasionally since if you have ever met a foreigner they generally do so. For instance Shampoo saying "wo ai ni"(I love you in mandarin ) to Ranma is appropriate. Using it this way is to convey that the person is speaking their native tongue with the reader and the people hearing it consider it to be foreign. This is especially true for first person; for third person where the reader is supposed to know what is being said and the other characters aren't use "quotes with said in Chinese", italics, different color text, [in brackets],
One thing that does not translate well is honorifics. The use of honorifics can add a lot to the story with very little trouble and even if people do not know what they mean the story will still be readable. Personally I like when people do this since it makes the fic seem more authentic as well as gives more information on social structure/the person by their choice of honorifics. I'm not going to go into detail as to what honorifics to use since they are easy to find out. They aren't limited to just Japanese either many cultures use honorifics such as the Vietnamese, Indian, even English has and uses honorifics though they are rarely used in English outside of formal situations and children addressing adults (e.g. use Mr for your teacher).
Japanese pronouns have multiple meanings as well that really don't translate well since Japanese pronouns are not the same as English pronouns. Their pronouns function more like nouns for the purposes of sentence structure, grammar, and syntax. Unlike with honorifics I recommend that you do not use these. The reason I advocate against the use of these is because it may make your writing difficult to follow and the readers will actually have to know the meaning of them. If the reader doesn't know the meaning of an honorific they can still read and enjoy the story, the same is not true for the use of Japanese pronouns. Doing so can convey a lot of information for example depending on which pronoun used you can gather more information on social hierarchy, how the person thinks about the other person/themselves, age of person, and often their gender (the Japanese like the Spanish have many gender specific words). These are sometimes mistaken for or used as honorifics. An example of how it is mistaken is this: Ranma called Pantyhose Taro Pantyhose-temee in the manga. Temee is not a honorific it is a pronoun that works similarly to the word you in English but is also very disrespectful and would be somewhat similar to an English speaking person saying you as well as Pantyhose Bastard/Bitch- it can also be used as a standalone word (the name part is not required).
The next thing I'd like to discuss is insults/profanity. A cuss word can have many meanings depending on context, body language, etc. The choice of which cuss word used can also tell a lot about the person as well. For instance Ranma in the original manga occasionally uses profanity and otherwise derogatory language that is basically the same as cussing (VIZ toned it down since they like censoring manga). Depending on his choice of insult/cuss word you can tell the degree of how upset he is with the person. For instance when not upset with Happosai he uses ojiisan (similar to grandfather) and when upset he uses jiji (similar to old man and more rude than ojiisan) and when really upset he uses Temee (very rude form of you that is >= Bastard), etc. Several people may want to use the word Baka in their fics since Akane uses it a lot in the anime. Even though using Japanese cuss words in your fic is ok. I advocate against doing so. The reason for this is it's often better to use an English one since people will know it and your less likely to use it inappropriately. For instance the word Baka is a mild insult it basically means idiot, moron, silly, crazy, dumb-ass, etc., depending on context and body language. Saying this in say school won't get you in much trouble if at all. I've seen people use Baka as a substitute for stronger insults like Fuck you. It's not, Fuck you is much stronger and more personal than Baka and has sexual connotations that Baka does not. The Japanese do have words that are similar to Fuck You in meaning and they use the English insult as well, Baka is not it though. Also it depends on region for instance Osaka from Azumanga Daioh is less likely to use the word Baka she would instead use Aho since she is from Osaka/western Japan and Baka is a Tokyo/Eastern Japan insult (though this is less common now since Baka is the most common one used on Television).