This is why the use of water during oiling or conditioning is necessary. We want a water content, but we don't want downpour, showers, or puddles to wash our shoes. I still run my shoes down the running water everyday, using a dauber to get the dirt out. It certainly works better when there is a waterproofing cream.
Don't really get the disbelief and what you mean here.
I don't know that running your shoes under the water is great for cleaning them. I would think a good brushing is enough. Also, water has too high of a pH to be optimal for leather.
I just don't believe that oxidation and an oil turning rancid is necessarily different. I think it is semantics, rancid is something lay people use to describe an unfavorable condition of something whether that is a smell, or appearance or something, but the fact is an oil going "rancid" is due to oxidation. I've never read aromatic oils inhibiting oxidation. If you have some literature on that, I'd love to take a gander.