Are bitcoin exchanges all connected to each others? or just close platform I wonder these exchanges, e.g. mtgox , bitstamp, bitcoinChina...etc, are they using API to connect to each others? 

or they just closed exchange, the price sync are from the free market?
Prices are determined by free market forces. The free market prices coins different on each exchange due to liquidity, fees, fiat conversion options, and terms. Prices follow similar patterns over time, but it is traders that determine what the price is.