should both engine fans be running when the AC/Heat is off?

If the heat sensors behind the fans are closing and running the fans, then there's a lot of heat coming out of the engine. This is either normal or the engine is low on coolant or hasn't been flushed or changed in way too long. 

depends if you want air circulating or  not .

Since those are for cooling the engine, I'd say it would not be uncommon.

Yes Common on vehicles with electric fans the Engine hets up when Switched off the Fan keeps the Engin at a Normal temprature

With AC ON BOTH vans should be RUNNING! With the AC OFF< the fans are engaged from the E+COOLING FAN SWITCH! SO MANY cars get BAD ones with time that I recommend replacing them at 100,000 mile intervals! >>>ALSO power wash  your engien with GUNK ORANGE ORIGINAL engien cleaner at the DIY car wash! FOCUIS on the space BETWWEN the RADIATOR and the AC condenser where leaves, twigs, DEAD GRASS, animal NESTS and animal DROPPINGS have COLLECTED for years! this will improve the AIR FLOW and keep the engien running the COOLEST! Also BAD OIL choices wool make COATINGS on the inside of the ENGINE and THAT will hold in HEAT as well! USING MODERN SYNTHTIEC OIL with the proper SPEC NUMBERS is the best you can do! PENNZOIL ULTRA euro and ULTRA PLATINUM a warranty out to 500,000 MILES! It WILL keep your sensors FREE of deposits like TAR and VARNISH and WAX< and SLUDGE! NOTHING is BETTER than THAT! >>>IF YOUR ENGIEN IS OVERHEATING for some reason the FANS should and WIL go on and STAY ON til the engien gets BACK to NORMAL! 

it would have to be hot hot for them both to be on with out the aircon running. Can you see what the engine temp is in engineering mode if its a gm car or on a scan tool of some description personally I use torque on my android stereo to see what my Toyota is doing.

The fans are activated by ENGINE temp. the climate control isn't the issue.

Only if the motor is getting too hot...OR if you have the air flow set on defrost/floor. Many cars automatically turn on the AC in that position even when the AC switch is off.

Depends on the heat of the engine.  And that can depend on the outside temperature , but more on how hard the engine is working.

They should run when the temperature sensor signals the computer to turn them both on, AC on or off.