You have lots of options. It depends on what you want to do.
Download qt client and sync.
Click receive.
Click new address and label it something like 'coinbase payment'.
They send money to that address.
This is one valid option.
Yes.
Nothing happens "instantly". Even light doesn't travel across a room "instantly". Everything takes some amount of time.
Depending on a variety of variables, it can be as fast as a fraction of a second. Somewhere between a few seconds and a few minutes is more likely. If coinbase suddenly experiences an issue (for example if they are hacked and their bitcoins are stolen just as you are getting ready to make the transfer) then extended times from a few hours to never become possible.
Possibly. It depends on what you are attempting to secure yourself from. In reality, it would be better/safer to create a password on your wallet BEFORE clicking "new address". Even then it's possible, if the computer where you've installed bitcoin-qt is compromised, that your bitcoins could be stolen (since the thief could acquire your password and wallet.dat file from the copromised computer. It would be safer to generate the receiving address on a computer that has never been connected to the internet and never will be. It's up to you to decide how risk tolerant you are, and how much inconvenience you are willing to put up with for the sake of security.
Randomly.
No.
Sure. It's your money. Do what you want with it.
Not necessarily. It depends on what you are trying to accomplish.
Sure. You can create as many wallets as you like, and each wallet can have as many receiving addresses as you like.
You're welcome.