Well done Masaya for practicing your writing skills! I will correct you a little bit...

I will start write my diary. (I will start writing my diary)

Hi!
Thanks for reading this notebook.
So I will start write my diary.maybe.. (So I will start writing my diary.)

About my yesterday. (I'll now write about what I did yesterday. OR Write the title "Yesterday")

Yesterday I wake up at 7am. (Yesterday I woke up at 7am.)
Then I did learning english lesson at 7-8am. (Then I had an English lesson from 7 to 8am.)
It finished later I went to my office.It spend time for 1hour. (After it finished, I went to my office for 1 hour(??)
I little busy yesterday at work. (I was a little busy yesterday at work) *Do you mean you were busy or not busy? :)
I did ate lunch 12:00 (I ate lunch at 12:00.)
I came back my home. (I went back home.)
I did learning english lesson at 10-11pm (Then I had (another) English lesson from 10 to 11pm.) *You can use 'another' here :)
I went to bet.I slept. (Then I went to bed (and slept.)* You don't need to write 'and slept' but you can if you want to :)

Thank you reading my about yesterday!! (Thank you for reading about what I did yesterday!!)

*I hope this correction is helpful for you*

I will start write my diary.  > I will start writing my diary, or, I will start writing a diary. 

Hi!
Thanks for reading this notebook.
So I will start write my diary.maybe..  > I will start writing my diary, maybe.  

About my yesterday. > For this you could say a couple of things. "About Yesterday." or maybe, "  About my day yesterday." 

Yesterday I wake up at 7am. > Wake is present tense, so this is a mistake. When you use wake its more like..." When I wake up, it is still early morning." Here are some things you could have said here.

"Yesterday, when I woke up, It was 7 A.M."  or  " Woke up at seven." and it would be understood.

Then I did learning English lesson at 7-8am. > It seems you are just a bit confused with phrasing things, but it is understandable to a native speaker I promise! I have a couple ways you could have said this.

" After I woke up I took an hour long English lesson."   "Then, I did my English lesson from seven to eight."    "Then I took an English lesson from 7 A.M to 8 A.M 

It finished later I went to my office.It spend time for 1hour. > I am not  sure what you were trying to say here. But, It seems like you were trying to say you went to your office after you did your English lesson for one hour. If that is what you were trying to say, here are some ways you could say that! 

"When I was finished with my English lesson, I went to my office."    "After my lesson, I went to work."    "After the lesson, I went to my office." 

I little busy yesterday at work. > It seems you are missing words here, I will put down a few suggestions! 

" I was a little busy at work yesterday."   "Work was a little busy yesterday." 

I did ate lunch 12:00 > You almost had this correct. This is the proper tense! but with I did in front of ate, it is incorrect. It would be, I did eat.  Here are some suggestions for this sentence!

" I ate lunch at noon.  "   " I did eat lunch at 12:00."   "I ate my lunch at twelve." 

I came back my home. > You could just add one word. "I came back to my home." Here are some other suggestions. 

"I came back home."      "I got off work and went home."     

I did learning english lesson at 10-11pm > I already wrote about this mistake! 
I went to bet.I slept. > I went to bed, Or, I went to sleep would have been correct here. 

Thank you reading my about yesterday!! > I already talked about this as well.