I read that many silver dollars minted after 1850 were sent to China, but did some circulate in the U.S. also?

There were only 7500 made that year. Seated dollars never circulated to any great extent in the East, though numbers were in daily use west of the Mississippi. The Civil War further restricted their circulation as the numbers of business strikes and proofs struck contracted sharply. Bullion buyers snapped up most new silver coins for export as fast as they were made. These coins were shipped overseas for melting, and the only U.S. Mint product most citizens saw were the new bronze cents. Coin collectors derided the Mint as “Uncle Sam’s copperhead factory.”