Please see the following article which will answer all these questions and more:

Introducing the Motif XF Effects

If you get stuck or still have questions post back here.

Thanks Phil. I'm asking this question because in the diagram there are two inputs that are going to the System effects module. If that is true, one should be able to get the output of the MOTIF XF through Assignable R/L jacks and feed it back to the INPUT. If we had Compressor effect in the System effects and the diagram works as it's depicted, then sidechaining is possible.

Is it technically impossible to add compressor effect in the system effect category? because it's available everywhere else!?

It is available wher it can be inserted inline with the signal. The article spends some time defining the difference between System Effects, which work on a Send/Return basis. Where you send in a subjective amount of signal to be effected and you leave an open path for what is called the DRY signal.

Compressors, like EQ's, will never be found in a situation where you subjectively process some of the signal. 100% of the signal must pass through the device to avoid phase cancellation. So by definition Compressors and EQs will never, ever be found in a Send/Retrun scenario. Never ever as System Effects.

Insert Effects are literally inserted inline with the signal they process
System Effects are routed to on a per channel Send amount, Stereo Return basis.

Please read the article.

Thanks Phil. I'm no expert in this area I'm talking about and need some help 😛 I read the article and I understood it up to some degree. The part that I specifically didn't understand is the phase cancellation part. I know very little about mixing and effects. Is phase cancellation necessarily bad? Can we take advantage of it to produce a cheap sidechain effect (this is what I'm looking for)?

I read this article before:
Sidechain Compression Alternative

And I was thinking if it's possible to do it on MOTIF XF. Is it possible to do what is described in the link on MOTIF XF? I was thinking to reroute the assignable output of kicks and feed it back to A/D input but then I don't know where to go from there in the case if it's possible...

Is phase cancellation necessarily bad? Can we take advantage of it to produce a cheap sidechain effect (this is what I'm looking for)?

phase cancellation, in this case, is a bad thing, yes. I spent my early years in the recording studio, so not only is this like second nature, I also used to teach audio engineering at the college level so I understand that it's like a foreign language to many. The fundamentals remain the same.

But as musicians we should become familiar with the proper use of effects. Send/Return effects versus "inline" effects. It very common practice in recording studios to print things like vocals dry. Any reverb is in the monitor mix only, reason being, the amount of reverb should be determined when all components of a mix are assembled. Besides the amount of reverb that makes the singer comfortable is rarely appropriate in the final mix. And once recorded with reverb it's almost impossible to remove it. This is one of the reasons why the inline (Insert Effects) get fed to the individual direct outputs, and the System effects are not. Reverb amounts are determined at final MIXDOWN.

Phase cancellation, the bad kind, destroys the definition of the sound, a weak boxy sound is often the result. Side chain effects require a routing situation where one signal is used to influence or modify another.