About the cable: the 75 ohm rating refers to its operation at radio frequencies. Hi-Phib's response is of course the correct one (that of caution), though I can attest to the fact that I have never had problems with RG58 and RG59 in terms of signal loss or filtering.
The short wire is indeed for connecting to your motor unit or turntable chassis and may not be required, but it is there just in case. The images you posted remind me that the SME arm is ready earthed when you use its original plugs and leads, so I would suspect a fault if you are getting hum.
BTW, what cartridge are you using? I recall a comment I read about some cartridges being reknowned for picking up hum.