What about Llunch?

Lunch shouldn't be capitalized here.

aA soba and yogurt.

Make sure to capitalize the first letter in every sentence :)

a buckwheat noodles!¶
a Buckwheat noodles!

Capitalize the first letter of the sentence, in this case Buckwheat.

bOh, good!¶
b Oh, good!

Make sure at the least there is a space between the the b and the first word as at first I was confused at what word "bOh" was meant to be. :)

a Salmon grilled salted.

Here I would say "Grilled salted salmon" as adjectives in English should be before the noun they are modifying.

B: I didn't eat breakfast too, had shrimp pasta with cream sauce for lunch, and steak, hashed beef rice and cabbage for dinner!¶
B: I didn't eat breakfast either; I had shrimp pasta with cream sauce for lunch and I had steak, hashed beef rice and cabbage for dinner!

In the section "I didn't eat breakfast too," I suspect you were trying to say that the person you were talking to didn't eat breakfast just like you. In that case, it would make the most sense to change the "too" to "either".
I also really like here how you used "B:" to separate the person from the sentence, it makes it much easier to read.
In a case where you have a section of the sentence that can function as a sentence on it's own but you don't want to sentence to end, you need to use a semicolon (;) to seperate those sections. "I didn't eat breakfast either; " and then add the rest of what you'd like to say.
Rather than just saying "Had shrimp pasta", you need to add "I" because otherwise we have no idea who had the pasta.
Whenever you switch from talking about what you had from lunch to dinner, I recommend saying "I had" again, just so that we know that the foods before were for lunch, and the food after is food for dinner.
Make sure the only places you put commas (in this sentence) is when you are listing nouns.

A: You had bid dinner!

Truthfully, I'm not sure what usage of bid you are trying to use here as it's a bit confusing. I can't tell whether it's a typo for big or whether you had meant to say that you "bid for" that dinner. In case you meant to say bid, the context is kind of lacking there.

B: Oh,yeah?¶
B: Oh, yeah?

Make sure you add a space after a comma.

Cause I was starving.

Cause /is/ used in slang for because, but it isn't proper grammar to start a sentence with "because" in any case. That doesn't mean it isn't done, but I'd be careful about doing it in formal settings especially as 'because' is generally used to connect two ideas. Without the first idea, it's harder to know why the second idea was done. "I ate because I was starving." 'I was starving' is adding information onto why the first action "I ate" was done. If you wanted to use the slang "cause" here I'd say "I ate cause I was starving."
Your sentence is used, I'm sure even I've said it before just like that, I'm just trying to impress that it's not technically good grammar. When I use language like that in front of some people (particularly older people) I definitely get a frown or two sometimes lol.

a I ate some soba and a yogurt.

I know in Japanese you often don't use I (私、僕）etc, however, in English we normally keep it. Also we would say some soba, since you didn't eat every soba noodle in the world. I put a yoghurt because in Australia we often buy yoghurts in individual containers, but I don't know if it is the same in Japan- you could either say a yoghurt or some yoghurt

b What's soba?

b Oh, good!

EA They are easy on the stomach!

a I'm only eat things that are kind to my stomach.

This sounds more natural

b Yeah, that's right.

This sentence is not needed and feels unatural to say. In English we don't use as many phrases as Japanese does to let the speaker know we are listening.

a Salmon gGrilled and salted. Salmon

A: Japanese style grilled salmon is salted salmon.always salted

This feels a little unatural. I think what I have written would make more sense in English, though it does slightly change the meaning of what you wrote.

B: I didn't eat breakfast too, then I had shrimp pasta with cream sauce for lunch, and steak, hashed beef rice and cabbage for dinner!

A: You had a bidg dinner!

B: Oh,yeah?

Saying "oh, yeah?" sounds like a slightly agressive response to this quesion - though it depends how you say it. This is the same point I made earlier but also applies here, In English we don't use as many phrases as Japanese does to let the speaker know we are listening.

Let me know if you have any questions about this :-)

Cause I was starving.

Cause is very casual, in conversation this is great usage. If you were writing something formal though make sure you write because

a sSoba and yogurt.

b What's soba?

a bBuckwheat noodles!

b Oh, good!

a I'm only kind to my stomach.

a Salmon, grilled, salted.

B: I didn't eat breakfast too, either, had shrimp pasta with cream sauce for lunch, and steak, hashed beef, rice and cabbage for dinner!

Unless "(hashed) beef rice" is indeed the name of the dish...

A: You had a bidg dinner!

B: Oh, yeah?

CBecause I was starving.

People say "cause" or "coz" when they mean because, in writing that doesn't look that great.
The word cause has an altogether different meaning (both as a verb and a noun, neither of which fit here).