Say I buy a Bitcoin from a specific market, like BTC-e, and it goes into my wallet. Is it possible for me to transfer that Bitcoin from its current wallet (BTC-e) into a wallet that I have on another market, like LocalBitcoins? If so, how can I do that and is there a fee?
Also, do all markets (BTC-e, LocalBitcoins, etc.) allow you to withdraw a Bitcoin from your wallet and exchange it for cash?