I have downloaded the "Bitcoin - Wallet" It did an update of like 300 weeks I believe over night so it's finally done today.
1. To find out my wallet code do I just click on "Receive" and it will be under "Address"?
No, "Address" will list addresses where you've sent Bitcoins in the past.
"Receive" is the list of your Bitcoin addresses, which you can use to receive Bitcoins.
By the way: There are light local clients that don't require you to download the whole blockchain (history of all Bitcoin transactions): Electrum and Multibit
Now my understanding is before doing any kind of mining.
I would advice you not to go into mining (or at least wait until you really understand how Bitcoin, difficulty, mining and so on work)
As the articles I've read online in the last 3 days show that people are making a ton of money mining but it all seems to good to be true really
Most people will be worse off than if they bought Bitcoins and hold them instead of buying mining contracts/buying mining hardware.