I did this work.  Я сделал эту работу.   Correct!  However, you could also say, "I have done this work", which has a different nuance).  The past simple tense simply tells us that at some time in the past, you did something.  It could have been yesterday, or it could have been 50 years ago.  It may still be important in the present, or it may not be important.  We don't know. //  The present perfect tense suggests that what you did in the past is still important in the present. Example:  "I lost my car key this morning."  I would say this if I lost my key, but later found it, or had another key made.  The fact that I lost my key this morning is no longer important to me. ....   "I have lost my car key" suggests that the fact you lost your key is still important to you; for example, you've lost your key and now you can't get into your house.  The present perfect "I've lost my car key" can also suggest that you had a certain experience during your life.  Example:  A:  "I lost my son years ago."  B: "I know how hard that is.  I have lost a child too."  

I have done this work, before he came.  Я сделал эту работу, перед тем как он пришел.   Incorrect.  You used the "present perfect" tense.  However, it is not correct to use the present perfect tense when the sentence refers to a specific time in the past.  Here, the sentence refers to a long, but specific, time in the past:  "before he came".

You could use the "past perfect" tense:  "I had done this work before he came."  The past perfect tense is appropriate when there are two actions, one of which happened before the other one.  Here, you did work; and later, he came.

How to write this correctly? Explain to me the meaning.

I did this work. Я сделал эту работу.
I have done did this work before he came. Я сделал эту работу ,перед тем как он пришел.
Why do Russian start two sentences spelled the same, and English different?

You can start both of these sentences the same way in English. "I have done this" means almost the same thing as "I did this", but a native speaker would say, "I did this" in both of these sentences.

I can think of only a few rare instances when an English speaker might say "I have done this". It is very formal and unnatural to say.