Talking Cargo Question
 

This may sound a little odd, but can passangers be hauled on Cargo Flights? I know ocean liners will sometime accomodate passangers going from the US, Canada to the UK or Europe. But do Aircraft Freight Movers do the same?

Not usually.
Depends if a jump seat is classed as a pax.

I know on a couple of horse charters where the grooms usually accompany the livestock, but again, not sure if that counts.

A company certified for cargo ops only cannot sell seats. We do carry animal handlers, couriers, customer employees on occasion.

I think the keywords you are looking for is "fair paying passengers"
As soon as you pay a fair for airline travel it becomes a passenger flight and a whole new set of rules come into play.

Many of the products carried on cargo aircraft have associated hazards. In small quantities these are sometimes acceptable but in larger volumes they are deemed only suitable for freight flights. This therefore would often preclude fair paying passengers on this basis alone.

That reminds me the batteries in my geiger counter have gone again.....

Do EVA Air have some 747-400s that are configured for both PAX and Cargo?

Eva may. Asiana and Alaska do for sure. There are probably others.
Actually, virtually all airlines carry cargo in the belly holds. Those mentioned above also have some number of "combi" airplanes that have the main deck divided for passenger and cargo use.

Technically, grooms & couriers on all-cargo flights are "additional crewmembers," not passengers.