Output connections

Your KPA outputs wether from the XLR or TRS connection (both balanced analogue audio) go into your chosen monitoring device. It could be as an example a monitor controller hooked up to your active or passive (via amplifier) speakers, or alternatively into a mixer (control out of the mixer to amp or active speakers). This would allow you to monitor while you are playing or profiling as well as re-amping.
If re-amping your D.I. signal typically goes from your audio interface/soundcard to your re-amp device, from the re-amp box connect the instrument out to the KPS input (where you would plug your guitar) via an instrument jack. The KPA outputs then go to back to your audio interface for recording and monitoring (careful with loops, turn your monitors down just in case...)
If you want to use the digital SP/dif bear in mind that the KPA is always the master and your interface is slaved to the KPS incoming clock signal.
Hope this helps.

Sorry forgot to add, regarding mono or stereo, it depends. Profiling in the KPA is (at the moment) mono only therefore it would probably make sense to monitor in mono unless you are using stereo effects in the KPA effects section.

The line outputs need to be connected to whatever you are using for monitoring during profiling, either active or passive speakers via a monitor controller or a mixing board so that you can switch and hear between your amp and the KPA.