Fonzirelli, Doctors here are compassionate towards people who get relief from medical marijuana. I experience similar issues as you, anxiety and depression, also insomnia. As long as you are honest with your doctor and let them know that mj is helping, they will be more compassionate.
There was no background check for me.
In southern california, we dont really go by a card, you just get verified by your doctor at the club you go to.
As far as moving to california for this, there are many states that offer medical marijuana, I cannot speak for them as I have only experienced california's mmj. But before just diving in and moving, I would suggest taking a week off and fly out here. Spend some time out here, the people are much different then east coasters. That may take some time to get used to!