Is www.soundike.com legal in the US?

If this program copies music without being a license from ASCAP or RRA or another licensing organization it's probably a per se infringing program under the Digital Millenium Copyright Act. That it's from "Russia" andn may be legal there does not make it legal here. You would be civilly liable for copyright infringement if you're lucky, and possibly criminally liable if you are copying and distributing those copies in the US. Copying is an infringing act unless it falls into a very limited fair use exception. Disclaimer. I am not your lawyer. The information provided is merely for educational use. Contact a lawyer in your state.

Chances are it is based in Russia for a reason - as a US citizen you would be using that service at your own risk.