Lastly, in coinbase, it seems each purchase of mine has its own identifier and its own "bc address" which, if I am not mistaken, is a wallet identity hosted on the coinbase server. Are these the numbers that others can send bitcoins to in drawings and rewards seen on this site?
I believe they are permanently associated with your account, but you should really check with coinbase. Having said that, it is unwise to store your bitcoins in someone else's wallet. Every few months, there is a report of an online wallet being hacked or lost and customers losing all their bitcoins. No site is immune, though some might be more susceptible than others. If you store your bitcoins in your own wallet, and you encrypt and back up your wallet (in that order) you will be much safer.