Write aA letter to my friend who went to study at London A letter to my friend who went to study at London

The correction above is just a description of what you're writing, but if you want to make the title a command, you should say "write a letter to your friend who went to study at London". If you say "my friend" it sounds like you're telling yourself to write the letter.

It whas abeen long a, long time. It has been long, long time.

It whas a longbeen a long time. It has been a long time.

I hope you are fine. I hope you are fine.

Since you went to London, we didn't talk haven't spoken (together). Since you went to London, we haven't spoken (together).

Since you went to London, we didn't talk togetherhaven’t talked. Since you went to London, we haven’t talked.

So i, I want to know all about your new life. So, I want to know all about your new life.

So iI want to know all about your new life. I want to know all about your new life.

What's about London, it isLondon like? Is it a beautifull town? What's London like? Is it a beautiful town?

I think it's more technically correct to write these as two separate questions, although in more casual contexts, like when texting, a comma would probably be fine. Also, I think generally people would refer to London as a city - towns are usually not that large.

What's aboutHow is London, it? Is ist a beautifull town? How is London? Is it a beautiful town?

And the people, are they nice withto strangers ? And the people, are they nice to strangers?

Just saying "people" sounds like you're talking about all people abstractly, whereas "the people" makes it clear that you're talking specifically about the people in London.

And people, are they nice withto strangers ? Are they nice to strangers ?

AWhat about your school, d? Do you like it? What about your school? Do you like it?

AboutDo you like your school, do you like it? Do you like your school?

Do you have you new friends? Do you have new friends?

Do you have you new friends? Do you have new friends?

wWhat are their names? What are their names?

wWhat are their names? What are their names?

TDo the teachers give lessons comprehensibly? Do the teachers give lessons comprehensibly?

The correction above is grammatically correct but sounds very weird. A more natural way to say this is probably "do the teachers teach well?" or even just "are the teachers good?"

Teachers give lessons comprehensiblyHow are the teachers? How are the teachers?

And the food, do you like London's foods? And the food, do you like London's foods?

The difference between "food" and "the food" is the same as the point above about "people" and "the people". Although "London's foods" is an understandable phrase, a more natural way to say it is "and the food, do you like it there?"

Do you do any exercicese? Do you do any exercise?

Do you do any exercices? Do you do any exercice?

If yes, Which so, what? If so, what?

If yes, Which ones? If yes, Which ones?

Abouts for me, iI am very fine. As for me, I am very fine.

Since you went, i goleft, I have been going to Paris University to do Mmathematics. Since you left, I have been going to Paris University to do mathematics.

Using "have been..." shows that something began in the past but continues into the present, so is quite useful in the context of a letter. So, for example: "I go to Paris University" - you go there now but this gives no indication of when you started going. "I went to Paris University" - this sounds like you no longer go now. "I have been going to Paris University" - you started going in the past, but you still go there now. You can use this with basically any verb. For example: "Recently, I have been playing a lot of football" - I started in the past ("recently") but I still play football now. "Since then, you have been swimming a lot" - after some point ("then"), you started swimming and you still swim now. "He has been eating a lot of chocolate" - he started at some point in the past and still eats a lot of chocolate generally now.

I began well and iI like this modulcourse. I began well and I like this course.

"Module" usually refers to a smaller part of something I think. For example, in a university course you may take lots of modules or classes.

I have meet many peoples here who are my friends now. I have met many people here who are my friends now.

We pass much time together. We pass much time together.

"We spend much time together" might sound a bit more natural.

I waitill wait for your response, in a short time. I will wait for your response, in a short time.

Take care of yourself. Take care of yourself.

Or just "take care".