Sounds like Sweden, except the chaotic booking system.

I don't think I've ever seen a diesel train, ever. In fact, for a long time I was (blissfully) unaware of their existence and the fact that they do exist still surprises me...

Sure, but that's helped by things like the biogas train that's fueled with confiscated alcohol instead of diesel.

Are they diesel electric? I think that's what parent meant.

Diesel engine driving electric motors (for torque and efficiency)

  I think that's what parent meant.

Doubtful. Electric in EMU or in the context of Caltrain electrifying means pure electric traction power. In the United Kingdom I think they make some differentiation between a DMU (diesel-hydraulic, like an automobile with an automatic transmission) and DEMU (diesel-electric like a locomotive). There were diesel-hydraulic locomotives along the west mainline for a bit, but in general diesel-hydraulic locomotives were fairly uncommon.

If it's being called electric it's not going to have a diesel engine of any sort.