Simple answers to your VERY COMPLEX questions.

1. Get the AA card.
2. You can get elite status 2 ways on AA. The easy way is B.I.S. So book and fly lots of flights. Or, as an alternative, get the AA card and spend about $900,000 on it (assuming you get the 100K sign up bonus). By getting 1M miles you will earn lifetime gold.
3. For your third question by taking the step of spending $900,000 will get you the tickets you want.