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I don't have any spare arduino mega and ramps to check this out (burned 2 arduinos in past two years :D), but I am almost 100% sure Vref on drivers can be changed without motors running as it is recommended to turn the motors off (for eg. in Pronterface), when you change the Vref. The motor even don't have to be connected to the driver when you set the Vref.

Yes you can measure Vref between the center of trimpot and any GND you have in machine. So "-" of PSU or the metal cover of USB connector is just fine. BUT ... Strange is the fact you cannot measure any voltage between trimpot center and GND pin on driver. Please check with electronics disconnected from any power supply if GND of driver and other GND ( or "-") on ramps is connected (with multimeter it shall look like short circuit). If GND is not connected to driver pin, there is probably some problem with ramps or driver, like something is not soldered well.

Yes DRV8825 have opposite direction of trimpot compared to A4899. It goes to minimum when you go clock wise.

On this picture https://a.pololu-files.com/picture/0J4233.600.png?665d623ba84232de64511d8aa6644836 is schematic of the driver. GND pins shall be connected together and to "-" of PSU. MS0, MS1, MS2, will be either open or connected to Vdd = fault pin on DRV8825 (depends on microstepping you have set). Step, Dir, Enable are connected to microcontroler (hard to check). Sleep and Reset are either joined together or connected to Vdd (I am not sure here). A1 can be connected with A2 and B1 with B2 only when motor is connected (you can measure the resistance of the each coil here). Vmot is conected to "+" of PSU. Check other driver positions too.

No problem. I've learned a lot through helping other people out with ToyREP and this is just the kind of experience I am looking for ;).