going to tokyo for one week

I know this might asked a lot but i have an exception. I am going to stay at my friend's house. so i dont have hotel expenses. probably i will skip eating food outside sometimes too. but still how much money do you think i need apprx to survive in Tokyo Japan

It totally depends on what you plan to do while staying at your friend's.
Which part of Tokyo your friend's house is (maybe the name of the nearest station is helpful), what place you want to go, etc.

Is your friend providing food? Are you treating your friend for something? Are you purchasing souveniers?

What do you consider food? A plain udon can be 500 yen. An onigiri, 150 yen. A bowl of ramen 1200 yen.

Prices vary according to the food. Sushi is pricey. Even more so then land meat.

I usually allocate 600 to 800 yen a meal.
I multiply by three for the three meals per day. Sometimes I eat a light breakfast so I can splurge on lunch.

At restaurants, dinners are usually more expensive than lunch so you might want to have a save on dinner so you can have a similar meal but for half the price during lunch.

she does provide me with food actually, since i am gonna stay at their parents and they are native japanese and actually her grandmother is a chef so maybe staying at home will be better than eating outside... i do no get what you mean by "you are treating her with something" nothing particularly actually no... maybe i am a freeloader in Japan :D haha, I just have particular foods that I would like to try... the whole Asian Cuisine actually. So if we presume that I will eat breakfasts at home sometimes dinner and lunches too... and stay for one week Apprx how much would I need for a day

It's a bit awkward and inconvenient for the family you plan to be "freeloading" off of, especially considering you're a complete stranger. It would be a good idea to bring an omiage for the family as thanks for letting you stay at their place. If you leave a good impression and don't make things difficult for them, they're more likely to have you back next time you visit. For example, you might join them for meals if they offer but I wouldn't ever ask them to cook you meals. At the very least you can grab a light meal from the closest convenient store. You can also buy them dinner if they let you and you're feeling generous.

of course i will bring a gift to show that i am thanksfull but the thing is i still dont have a financial income since i am not a grown up so i dont think that i will make a generous act and pay the bill for the dinner sorry, but ive never think that eating with them would be disregardful, I mean I wouldn't force them to cook for me never that is awkward, but joining foods does not seem that awkward... or is it awkward in Japanese culture? because in our culture if you dont join to the meals you will become the black sheep of the family they might even gossip about it.
I've never felt that I should feel like a complete stranger after all they are my friends grandparents whom I heard really cool about these stuffs, so me eating in the house is not morally okay in Japan since i am a guest?

In any culture it is only polite to bring the host a gift from your homeland, and contribute to at least one meal. You say you are not an adult but you must be old enough, I presume you are traveling alone. Yes, I'm sure grandmother will enjoy cooking Japanese meals for you, and you sound like you will be open to different types of food. However, you must have some money, you couldn't be going into Japan without cash, so if you were my grandson I would be suggesting you buy a nice dessert one night, or maybe some seasonal fruit to contribute. You don't have to buy the dearest, and you probably only need two pieces, as Japanese people slice fruit up for serving. You cannot take it for granted they want to feed you every meal, plus provide your accommodation free, and you want to be a good house guest, surely.

The above poster is correct. While I'm sure they don't expect you to pay for everyone's meals, it's good to at least provide a desert or snack at least once or twice while you are there.

I always give my homestay family a small pay for housing me whenever I go (about 20-30 in US dollars for each night I'm there) and I try to either cook one or two meals while I'm with them or just buy something that everyone can share and enjoy.

Remember, even though they are cooking for you, they still are buying extra food in order to feed you so it's good to try and pay them back in someway while staying with them.

Oh okay I see,
Not really me and my friend is going to stay over her grandmother, I am not total stranger for the family but for the grandparents yeah they know my presence but they don't know me personally.
And yea I don't even think that Japan will take me without no money, what i wanted to imply by freeloading i might eat sometimes at home i am not going to exploit their food everyday and stay at their home that would be rude. But to be honest I've never thought of buying a desert or food for them. You are right they are buying extra food for me it would be disgraceful... Thanks for your answers really helpful :3