I hope you find the corrections helpful. Feel free to message me in case you want me to explain the corrections in detail. :)

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In Sunday, me,Harrison,Johnny,Angel and Lee went to big city.

On Sunday, Harrison, Johnny, Angel, Lee and I went to a big city.

Now I well tell you what it happen in that day.

Now, I will tell you what happened on that day.

In Sunday 11:00 A.M. we went to big city, we meet at Tom’s world.

On Sunday at 11:00 A.M., we went to the big city.  We met at Tom’s world.

First we went to eat lunch, and then we go to play baseball.

First, we went to eat lunch, and then we went to play baseball.

Harrison hit one homerun.And I hit many ball but I can not hit homerun, and everyone said harrison is good at baseball.

Harrison hit one homerun and I hit many balls but I can not hit a homerun. Everyone said Harrison is good at baseball.

Next we go to play tom’s world, I and Lee play gun fight.

Next we went to play at Tom’s world, where Lee and I played gun fight.

Lee is very good at playing this, so we win many time.

Lee is very good at playing this, so we won many times.

we have go to play car racing too, I win lee two time, and he win me one time.

We have gone to play car racing too. I won against Lee twice, and he won against me one time/once.

in 3:oo P.M.we go to eat ice cream.then we go to see some books.and we good home.
This is my wonderful day in big city.

At 3:oo P.M., we went to eat ice cream, then we went to see some books, and then we went home. 

This is my wonderful day in the big city.