1. If I have a Montage 6 as a secondary/ slave- keyboard, is it possible to play sounds generated by the Montage 6 on my 88-key stagepiano and at the same time play another sound locally on the Montage 6 also generated by the Montage 6?

Yes. This is accomplished by selecting the appropriate “MIDI I/O Mode“

2. If this is possible, is it then also possible to use splits- and layers of sounds generated by the Montage 6 on both my 88-key stage piano and locally on the Montage 6 at the same time? For example, can I play a Montage piano sound layered with a string/pad sound on my 88-key stage piano and at the same time play a Montage brass and organ sound with layers and splits locally on the Montage 6 keybed.

That will depend on your unnamed 88-key stage piano.

Creating a MONTAGE ‘brass and organ sound with layers and splits’ is done by setting these programs (called Parts) with KBD CTRL active.
In order to trigger via MIDI ‘a MONTAGE piano sound layered with a string/pad sound’ from your external keyboard it would need to transmit on multiple MIDI Channels.

All Parts with KBD CTRL active (green) can be played simultaneously, (either from your external keyboard or with the MONTAGE keyboard).
How many MIDI Zones does your 88-key stage piano transmit on? That will determine what you can do.