Here are just a few preliminary thoughts :
The first thing you need to do before you start making too many plans is to find out
exactly[/b]what the Conservatory's entrance requirements are. You need to find out what the Conservatory's quota is for new students in any given year, and if there is a quota for foreign students. If they accept only a small number of foreign students per year, you might find your chances slim of getting in, realizing that there are always eighteen-year-olds with years and years of study behind them competing to get into good Conservatories.
If you feel that you can fulfil the requirements when you are ready to make the move, and that you have a chance of beating your competition to get in, then you also need to check with the Russian Consulate to find out what you need to do to be a registered alien while studying in Russia.
You need - obviously - to find out the costs of living and studying in Russia and, as foreign students have to do when coming to the US, you might have to prove your financial independence for the duration of your time in Russia to the Russian government before a visa is granted for your stay. One could be accepted for admission by the Conservatory but refused entrance into the country if one can't provide proof of financial independence for the length of the stay in the country.