I think Watson would be able to give it's real age by finding the information rather than recalling it, although it might get confused by progressive versions. AI can also produce a picture of a generic rabbit,
or cat as the case may be.
The thing that Watson (and AI in general) has difficulty with is imagination, it has no experience of the real world so if you asked it something like what would happen if you ran down the street with a bucket of water, it would be stuck. Humans who have never run with a bucket of water will automatically visualise the situation and give the right answer, just as everyone who read the question have just done so in their mind. OTOH a graphics engine can easily show you what would happen to the bucket of water because it does have a limited knowledge of the physical world.
This is the problem with putting AI in a box labeled "Turing test", it (arrogantly) assumes that human conversation is the only definition of intelligence. I'm pretty sure Turing himself would vigorously dispute that assumption if he were alive today.