When his food dish is in the kitchen, my cat only takes a few nibbles of food, then walkes away. But put the same dish outside, and he gobbles it down like it’s his last meal. Why is this?
Just a WAG, but if the cat wanders off and leaves food unattended outside, it may not be there when he gets back. There are other cats out there. Indoors he feels more secure and has no need to finish the bowl in one go.
I agree. It’s not a matter of “prefer” at all. In fatc, your cat would likely “prefer” to eat inside.
But why does my cat prefer (sic) to drink water from the bathtub rather than his dish?
If you are talking about a drip from a bathtub water faucet, it’s probably because he prefers moving water to still water. My cats drank from the tub all the time in the old house, so when we moved them into the cat suite, we bought them a water fountain. They love it.
Right, I concur. 
In fact during very hot days or when you’ll be gone for a while, I suggest leaving a drip for the “fuzzy buddies” to find.
Once, I left my uncle Osmond in charge of my three cats while we went to the beach. He was in the library, they were in the conservatory. When I returned home, there was a human skeleton seated in the reclining chair. I do not recommend this.