This is very helpful.  Thank you.

So it seems machines mine for nonces and get rewarded bitcoins. Once a nonce is found, the block is created which always has the new reward bitcoins and other transactions and the search for a new nonce begins. 

Mining cannot be done offline since every ten minutes you start searching for a different nonce.  Is that correct?

And if you find a nonce seconds after someone else you will most likely not get the reward because the majority of miners will start searching for the nonce following the block of the person that got there just before you.   Seems like there is a high frequency trading strategy here.  If you find a nonce, you are better off if you can propagate it faster than everyone else.