How do the Beech Bonanza's ruddervators work? When the yoke is pulled completely back, is it possible to use rudder?
In the Bonanza, a mechanical mixer controls ruddervator movement based on pitch and yaw commands. Here's a typical V-tail mixer (this is not of a Bonanza though):
There are two rods extending off to the left of this photo that connect to the actual ruddervators. Rightward motion of the top rod (due to either rightward motion of the entire mixer assembly due to a pitch command, or clockwise rotation of the assembly due to a yaw command) will deflect the ruddervator one direction; leftward motion deflects it the other direction. Similar for the other ruddervator connected at the bottom.
I can't completely answer the second part of your question, whether yaw authority is reduced when pitching or vice versa. It depends on where the limit stops are installed in a Bonanza. If the stops are set on the ruddervator side (left side in photo above, so that the mixer's range of motion is limited by its leftward connections), the amount of available rudder will be reduced when pitching. (Sorry I can't answer that part of the question, but I thought the information about the mixer would still make a useful answer.)
The airplane is obviously designed so that sufficient authority is available in all situations. (This means making the two fins of the V longer than those of a traditional horizontal/vertical stabilizer design so that similar control surface area is available.)
A paragraph in Flying the Beech Bonanza explains the ruddervator operation:
The following facts from the Shop Manual for the V35B illustrate how the control mixer and ruddervator stops allow differential ruddervator displacement. With full up elevator and no rudder input, the left ruddervator will be 22 1/2 degrees up. With full right rudder and elevator neutral, the left ruddervator will be 23 degrees up. And with full up elevator and right rudder simultaneously, the left ruddervator will be 44 degrees up. By contrast, the elevator of the A36 is limited to 23 degrees up and 20 degrees down, while the rudder is limited to 25 degrees left or right.
TL;DR On the Beech Bonanza, the yaw and pitch inputs are added, so that full back on the yoke gives about 22 degrees of ruddervator, and adding full right rudder would add 22 more degrees for a net result of 44 degrees up of ruddervator on the left.
I assume that the other ruddervator would be at 22 degrees up, though of this I am not sure.