Correct.
273:1
I don't really understand the question. At some point, the question will come up whether CAR2 can convey good title, and any disparity between her birth certificate and a driver's license isn't going to have any relevance to that.
Prove it to whom?
No.
No one here can intelligently predict what a hypothetical police officer will or won't believe in a hypothetical scenario that hasn't been described thoroughly. However, in over three and a half decades as a licensed driver, I have been pulled over somewhere between 15-20 times and have never once been asked about my social security number. Even if I had been asked, my response either would have been no or to recite the number from memory because I have almost never carried my social security card on my person outside my home.
Howzabout you explain the purpose of all of these random questions? Do you have an actual legal issue that you're dealing with?