AD8113 operating voltage
Yes, it means that with a +/-12V supply, it can only handle inputs in the +/-5V range.

That seemed strange to me also at first (I did not know this device before your question), because it is specified everywhere that the output signal voltage range is +/10V with 12V supplies. Then, I saw that this device has a gain of 2 on all its outputs (it doubles all output signals). So it is consistent.

And, as you noticed, the AD chip doesn't have bidirectional input/output ports (you can't switch input and outputs). Most certainly because of this x2 amplification gain stage, by the way.