How I can become the officer of Police, if I the Citizen of other country? I very much would wish to become the officer of Police of the USA.

Become a U.S. citizen!

Some police departments will hire non-citizens. I think non-citizens have to be permanent residents that are eligible for citizenship though.

Thanks! And please, one more question: it's possible for the foreigner to be arranged in FBI? Or the citizens who were born in the USA can be agents of FBI only? If isn't, then what I need to do to be arranged in FBI?

According to the FBI website, you have to be a U.S. citizen. Being born in a different country would not disqualify you.

Well, and what age restrictions at reception in Police of the United States?
In Russia for example: 18 - 37 years/

Most police departments in the U.S. won't hire you until you are 21. Many police departments in the U.S. do not have a maximum age restriction. Some do. It depends on the department.

Tell, please, and if I'm a foreign citizen have a green card then, I can become officer of police of the United States?

Yes, it is possible depending on the department.