I wanna continue to write daia diary in English everyday.

"dairy" - milk, cheese, butter, etc.
"diary" - a book or equivalent where you write about your day

It’sThey're very good!

Matching the plural on "noodles"

I think

"It was very good" could also work if you're describing your time eating them, as the time is singular, but then it would need to a be in the past tense as you're talking about a specific time.

Today is my first daiary entry.

or "Today is my first journal entry."

I wanna continue to write dairy ian English diary entry everyday.

I’ve been busy with work lately, but I’ll continue to try my best tomorrow too.

Today is my first daiary entry.

Diary is what you write in, and a synonym for journal. Dairy is a different word which defines the group of food/drink that involve milk (milk, butter, cream, yogurt, cheese, etc.)
Your diary/journal is what you write in, but each time you write in it, it is your journal entry.

I wannat to continue to write dairyjournal in English every day.

"Wanna" is slang for "want to," but is not grammatically correct English.
Journal can also be used as a verb (to journal is to write in a journal) and fits most naturally here. If you did want to choose the word diary, you could say: I want to continue writing in a diary in English every day.
"Every day" means each day. "Everyday" is used as an adjective in a different sense, to be used for items that are both casually and often used, "These are my everyday slippers."

I’ve been busy with work lately, but I’ll try my best tomorrow to journal too.

It's good to repeat what you are referring to here since there was a small detour on other subjects.