I have edited insert a, insert b, chorus and reverb of a voice in voice mode and I have stored it... but when I use it in song/mixing mode, chorus and reverb parameters have not been stored. Is there a way to save all the parametres of the voice which has been edited in voice mode?

That is correct. The INSERT A and B are part of the Voice... the System Effects (Reverb and Chorus) belong to the System Mixer, not the Voice.
You need to spend time learning about the architecture of the synth. This article can help. It will explain why the Insert Effects can move with the Voice when you use it in a Part, and why the System Effects you Setup in Voice Mode no longer apply when you combine Voices in a Performance, Song/Pattern Mixing.

Introducing MOXF EFFECTS

In general, Insert Effects are the personal effects belong to the Voice (Instrument)... then the instrument is plugged into the System. Like a band member plugs into the bands mixer. Each channel of the band’s mixer has a Send (like an Aux Send) to the System Effects... Reverb and Chorus.
So yes, Insert Effects can be recalled in Song/Pattern Mixing, but all Parts share Sends to the same System Effects.

1) I have recorded a pattern with several voices (more than 4)... is there a way to use that pattern as an arpeggio? Or I have to choose 4 tracks of all that I have recorded?

No. Spend some time with the Manuals learn the difference between Arpeggios (which have the ability to adjust in real time to chord qualities) and Patterns (which playback prerecorded MIDI events as is) the maximum Arpeggios you can Control is four in Performance Mode. You are addressing all Parts of a Performance from the one keyboard. In Song or Pattern Mode you are setup to play just one Part at a time.

2) How I can play 4 arpeggios in the song/mixing mode and change the chords of the 4 arpeggios? I have achieved to play 4 arpeggios at the same time but I only can change the chord in one of them when recording.

You’d need to put all four Parts on the same MIDI Receive Channel.

You cannot Record multiple Arpeggiators simultaneously while in the Sequencer Mode. The Sequencer Mode is very much geared for one track at a time recording.

Direct Performance Record works, precisely because you are not in a Sequencer Mode when you are recording. You are in Performance Mode. In Performance Mode the MOXF Keyboard is controlling four Parts directly. The division to separate MIDI channels and the copying of the four Parts from Performance Mode to Mixing is all done in the five or six seconds after you complete the Direct Performance Record. The data is split out to,separate channels, the Parts are assigned separate channels to match the data generated for the Part... so they can be reunited in the Sequencer Mode.

You cannot Transmit on multiple channels in the MOXF Sequencer and if you put all Parts on the same channel chaos ensues with all the Arps. Trust me, that’s how it works.

Thanks for such an extensive and didactic answer.

I come from a simpler keyboard, and this is a new world... despite the fact of reading the manual I feel afraid of not understanding something and missing something important. Fortunately the three answers were the ones that I thought it would be... so I feel now more confident for following with the famous learning curve of this fantastic keyboard without having to disturb with so many questions.

Thanks again.