I had someone send me a valuable but small item from my old home in the States, to Turkey. I had them insure it for $1000 and the postage cost them $50. When it arrived today in Turkey, PTT (mail carrier) asked for $200 in customs fees. Is this typical for international mail? I haven't had this problem in other countries.
This is absolutely normal. Every country has a maximum amount allowed to be received in a country without the customs duty. The amount you have listed obviously exceeded that amount. And when you mail at least from the US your declared value of the merchandise/gift has to match the amount you're insuring the parcel for.
So since your amount exceeded maximum allowed import duty free you will pay whatever duty is imposed and any fines or penalties that laws will allow.
So 20% import duty is quite normal.
You can look at Borderlinx for the information on the maximum amount (though information for Russia is no longer accurate).