Write aA 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.

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

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

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

And the people, are they nice withto 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.

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

Do you have you new friends?

wWhat are their names?

TDo 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?"

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?

If yes, Which so, what?

Abouts for me, iI am very fine.

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

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.

"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.

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.

Take care of yourself.

Or just "take care".