Hi,

If the Beogram is connected to the Beomaster via the original 7 pin DIN cable, then this is already grounded, so no changes are needed to the wiring, as this is already grounded in the DIN cable.

If you are using the Beogram with a non-B&O pre-amp that has RCA inputs then it is always best to ground the chassis of the Beogram to the grounding screw on the pre-amp case to avoid unwanted noise.  This cable can be used for this purpose if you select the "external ground wire" option:-

The Beogram is hooked up to the Beomaster via the 7-pin DIN. They are both 5500 models and connect.

Do I still need to ground the beomaster somehow?

It should already be grounded but it would be easy to take a wire and touch it to the metal chassis of the receiver and turntable to see if it improves things.

Connecting the beogram to the earthscrew on the beomaster with a wire actually increased the hum.

Thank you for the help so far Steve and Bob. 

Ever since i acquired the turntable, the right channel has been significantly louder than the left. I set the balance to 3-o to account for this. Might these two problems (hum, balance) be linked to the cartridge?

Not sure about hum, but those old MMCx cartridges are pretty much all shot at this point due to cantilever rubber suspension failure.  This causes distortion and/or channel outage.  They can be rebuilt - the appropriate search keywords will return several posts on the topic.  Or Soundsmith in NY manufactures new 'SMMC' ones which are highly regarded.