1. Yesterday, my friend had been went to the in a hospital, because (or after) he had a heart attack alert.

OR My friend was hospitalized yesterday had been went in a hospital, after he had a heart attack alert .

2. He had felt a pain in his chest and his left arm.

AND

3. His wife called the emergency department and he was has been driven (OR taken by ambulance OR he was driven an ambulance took him) to a local in a hospital of the city.

(driven = your friend's wife called for help and was told to take her husband to the hospital, taken by ambulance/an ambulance took him = the hospital sent an ambulance when the wife called)

OR 2/3 combined. When he felt a pain in his chest and left arm, his wife called the emergency department and he was been driven to a local in a hospital of the city.

4. At For the moment, he is (OR For the moment, he is currently) passing undergoing several tests exams and controls.

(I agree with Susan612 about the use of undergoing. For a heart attack, your friend might have blood tests, EKG, imaging or stress tests and only the last one would a patient pass).

5. I hope that it will be is not serious and his your health will better improve .

Stay in Hospital

Yesterday, my friend had been went in to the a hospital, because he had a heart alert attack.
He had felt a pain in his chest and his left arm.
His wife called the emergency department and he has been was driven in to a city/local hospital of the city.
For this At the moment, he is passing several exams and controls.* <em>I'm not sure what you mean. We don't use 'pass' in the context of medical tests. You can say that's he's undergoing tests, or that all the tests have come back negative, meaning they haven't found anything significant wrong with him.</em>
I hope that it will be not serious and your his health will better improve.

Thank you for the correction of this imaginary paragraph.