1.
http://blockchain.info/ provides a wallet (and lots of data about the bitcoin transactions). The "Markets" tab used to be a version of what you see at
http://bitcoinity.org/markets (just reporting activity on exchanges, it's not an exchange).
2. I don't use a Blockchain wallet but I think the generic process is to establish at account at an exchange and then use a receiving address at the exchange to send from your wallet (or you can initiate the transaction at the exchange but putting in your Blockchain wallet's sending address.)
3. I don't know anything about mining but have heard that if you only order an ASIC now, by the time it ships, most of the financial benefits will have already passed you by.