Is Alice liable for that damage, given that she disclosed her
knowledge of the issue, the limitations of that knowledge, and Alice
and Bob agreed that Carol's professional decision was the basis for
the sale?
Alice is not liable for the damage.
If there is no Carol, and the sale is based on caveat emptor, which
may include Bob insisting on the inspection, but Bob does not do so
and makes his own personal determination, buys the car, and then it
fails catastrophically, does this change anything about Alice's
liability?
There is no liability arising from a breach of warranty under the Uniform Commercial Code in this case assuming that Alice is selling a used car and is not a dealer selling a new car (which carries an implied warranty that it is not defect and an express warranty as well). The applicable Article 2 of the Uniform Commercial Code has been adopted in every U.S. jurisdiction and is identical in this respect, although a few states would have consumer protection laws that impose special responsibilities in sales of used motor vehicles in particular that are not present under the Uniform Commercial Code that could apply in this case.
There might be common law liability for fraudulent concealment if the defect not disclosed is something that a seller in good conscience under accepted commercial practice in such sales would have been obligated to disclose (as determined by the judge and jury after the fact). The defect would also have to be a latent defect not visible upon casual inspection, to give rise to liability. Such a claim would also depend upon a determination of whether Bob actually relied on Alice's non-disclosure of the defect, and whether it was reasonable under the circumstances for him to do so in light of the fact that the car was already 20 years old. And, Bob would have to prove that Alice knew about the defect and its seriousness at the time of the sale, which would be hard to prove if she didn't affirmatively disclose this fact to him. These basic principles of liability are quite similar between U.S. states, although they aren't entirely uniform (in particular, some states would have a common law sale of used goods exclusion from fraudulent concealment liability).
Even then, whether or not the fraud liability would extend to the reduced value of the car without the disclosure, or would also extend to the personal injuries and property damage caused by the non-disclosure, could be a close issue upon which the law in different U.S. states would not be uniform.
It isn't impossible that the fraud claim would prevail, but both in pretrial motion practice, and on the merits at trial, this would be an uphill battle for Bob that he would be much more likely to lose than to win, even if he managed to overcome the procedural hurdles prior to trial to get the case in front of a jury.
Furthermore, most states would evaluate the case under a comparative fault regime, so some of the fault, and some of the damages, would be allocated to third-parties involved in the accident (if any) and to Bob's comparative fault in not being sufficiently careful by failing to have the car professionally inspected. In all likelihood, even if Bob won, he would not recover 100% of his damages.
Also, while Alice's insurance company would probably defend her in this lawsuit (on the theory that she was innocent of the claims), if Bob prevailed, Alice's insurance policies wouldn't pay anything that was owed on the claim. This is because the claim is based upon fraud, and since insurance is not allowed to cover successful claims that the insured made fraudulent statements as a matter of public policy under the law in every U.S. jurisdiction. So, Bob would be limited to collecting from Alice's income and assets that are not exempt from creditors.
