I have been learning English from my Psince primary Sschool. I have been learning English since primary school.

In English, "primary school" is not a proper noun, so it would not be capitalized. Use "since" instead of "from" when speaking about a period of time from past to present.

Then I wasI also learninged it in the institute, and I am still learning it. I also learned it in the institute, and I am still learning it.

"Also learned" is the correct past tense form to use. Use a comma before a coordinating conjunction (for, and, nor, but, or, yet, so) to connect two independent clauses (basically, to connect two sentences).

I like reading - it is easy for me as well a(so is grammar), but speaking and writing are hard. I like reading - it is easy for me (so is grammar), but speaking and writing are hard.

I like reading -— it is easy for me — as well as grammar, but speaking and writing are hard. I like reading — it is easy for me — as well as grammar, but speaking and writing are hard.

Be careful when using dashes. There are three different kinds and they have different uses. The type used here is called an "em dash." It is used in a way similar to parentheses to insert a phrase into a sentence. Even with this correction, the sentence is awkward. Another way you could write it would be like this: "I like reading. Reading and grammar are easy for me, but speaking and writing are hard." This is less awkward and more clear.

I want to pass the English exam for another institute, so I have to be able to describe a picture, compare two pictures, and write a letter and an essay. I want to pass the English exam for another institute, so I have to be able to describe a picture, compare two pictures, and write a letter and an essay.

When listing more than two things, make sure to put ", and" before the last item. The comma is not necessary, but it makes what you are saying more clear. You could also write your sentence like this: "I want to pass the English exam for another institute, so I have to be able to describe a picture, compare two pictures, write a letter, and write an essay." Since not all of the items in the list share the same verb, each item needs to have a verb ("write a letter, and write an essay").

AnThe essay is the most harddifficult task. The essay is the most difficult task.

You could also write it like this: "The essay is the hardest task."

AWriting an essay is the most hardest task. Writing an essay is the hardest task.

It sounds more fluent to specifiy the action since you are describing "it" as a hard "task". Task means to do something so by using that, the subject in front would have to be an action. Most hard does not work. Go with the hardest task or the most difficult task. Don't ask me why though. You'll have to Google this.