I set up 2FA on both, thanks....
1) You speak of a 'shared wallet'. I'm simple minded....does that mean it's in their wallet or mine? It can't be both. I don't want my bitcoin anywhere but in my wallet....I'm guessing the moment I get verified data that my wallet in coinbase has a bitcoin in it I need to immediately move the bitcoin into my wallet? If this is true then do I use the 'send money' icon as if I was sending it to someone else although it is just me sending it to me?
Thanks....
You've sort of got it.
It's their wallet. It's your BTC.
Coinbase doesn't generate a public/private key pair for each customer. They have a single public/private key (well that's simplistic, the probably have multiple wallets hot/cold/etc). Your balance is maintained by Coinbase keeping track of which addresses in that wallet belong to you.
There is no need for you to immediately move your money. Coinbase will keep it all straight. You can send/receive bit coin via your coinbase wallet. You can create new addresses and you can sign messages with your coinbase wallet addresses.
So, coinbase is more like a bank. At your bank, there is no drawer were just your money sits. The bank keeps track of how much of the money it has belongs in your account.
This is also the way the exchanges work. When you send money to an exchange, like BTC-e or Bitfinex or whatever, they give you a deposit address and keep track of how much BTC in their wallet belongs to you.
HTH