1. Is it OK if I just fill in those forms and have a doctor sign it ? Any specific requirement for the doctor? Or do I need to include all those supporting documents?
How you get the form done is up to you. As long as as doctor verifies the information as true, and signs it, it is acceptable.
2. I am going with my wife. She has got her F2 visa. Does she need to undergo the same process, with the same requirement?
We do not require anything for your wife, unless she is going to be a student.