One for each segment or you'll get the digit '1' much brighter than the '8'. With a singleresistor you are also depending on the segments being voltage matched or current willdistribute unequally between the segments (sometimes the output impedance of the driveris enough to help balance this, and usually the segments are identical LED dies from thesame batch so they are as well matched as you can get)There is an exception to this, if you are multiplexing such that only one cathode at a timeis active, one resistor will be fine. Normally though you would drive all the cathodeswith one anode active, then step to the next anode.Common cathode is exactly the same issues.
There's no such thing as a two-digit anode. Two digits each with a common anode, yes, exactly.