And can it gradually increase/decrease tempo in a song?

Previous gens had a knob you could turn to control the tempo in real-time for gradual increase/decrease. There's no such knob now and the main "real-time" control of tempo (without being locked into a particular screen) is either using tempo sync to an external tempo source or using tap tempo. The foot pedal can now be assigned to tap tempo which the release documentation say this can be used to vary tempo within a pattern. For me that would be a bit clumsy - to have any kind of control to tap a tempo in a controlled manner between slow to faster or faster to slower. By the nature of tap tempo, you have to give a couple taps before the system recognizes what the tempo is.

I don't think there are any tempo job menus for doing gradual increase/decrease similar to the crescendo job for volume. More advanced fundamental tempo control (or MIDI clock variation) has been avoided this gen as a built-in. For me, I think I would try using an external clock source and assign a knob to vary the tempo or use some external device's software to handle the clock movement I wanted. You have to cover synchronization of the external device to your keyboard's Pattern Sequence record - so it's not a walk in the park. After all, this is duct tape workaround stuff as the features are not built-in where having built-in controls would give a more integrated/straight-forward experience.

Can Montage record prog/bank changes in pattern or song recorder?
Is this possible? And can the montage also adress itself when recording/playing back the program changes?

While the Sequencer can record and playback Bank Select and Program Change information... those messages are not, however, generated by the MONTAGE front panel buttons.

If you have a composition to which you wish to insert Bank Select and Program messages you can use an external DAW to insert these messages. They will be read faithfully by the Sequencer. There is no event list in the Performance Recorder.

If you are playing a .mid General MIDI File, it will have a GM Reset command and a Setup Measure which will automatically select the “Multi/GM” Performance, then the Setup Measure will send in the author’s program selections for Parts 1-16, via standard Bank and Program messages per Track, CC settings to program Volume, Pan, Effect Sends, Filter settings, etc., etc., — if however you wish to change these selections, you must edit these in your computer DAW. The alternative is set the individual Part to ignore incoming Program Change and Bank Select messages... you can then substitute the internal program you wish to use in its place.

What you can do...
The Sequencer in the MONTAGE is a Performance Recorder... which means it is optimized to record your interaction with the Synth engine. The program you select is a Performance, while interacting with a Performance you have the ability to change which sound is active in any of the Keyboard Controlled Parts. To switch from a Piano to a Lead Synth, you would do so using Motion Control to switch active Parts — you could assign active control to change from an active piano to a synth lead using an Assign Knob, the Super Knob, an Assign Switch, a MW, etc., or a Scene change event can be used to switch active KBD CTRL Parts.

For example, I want part 8 to switch from a piano to a leadsynth on the third beat of bar 257.

The third beat of bar 257 can only appear in a MONTAGE Song (the individual Pattern Scene Length is maximum 256 Measures. Again, to actually enter the data into a sequence, you must do so external to the MONTAGE. Or send the message IN via MIDI.

And can it gradually increase/decrease tempo in a song?

Yes, real-time Tempo Changes can be recorded to the Song (Performance Recorder). You can change the Tempo during original (Replace) record, or you can add it, after the fact using Overdub Record.

Tempo Changes are not documented in the looping pattern mode as it requires a linear timeline (a measure at which to execute the change) and Song Position Pointer. You can however gradually or immediately enter Tempo Change during playback via the front panel.

Overdub Recording Tempo Changes to a MONTAGE Song
You can record gradual tempo changes using the DATA WHEEL, or you can enter it as an event at any specific point, by double tapping the TEMPO box — this launches the numeric keypad — type in your new Tempo, tap “Done” at the precise moment you wish to insert the Tempo Change Event.

Alternative options:
You can connect an iOS app that can send Bank Select/Program Changes on any channel... this can be used to input your information. You can select the Track you wish to insert the message, place the track in Overdub Record, enter the data where you need.

Drag n Drop your Song or Pattern using MONTAGE CONNECT __ edit in your favorite DAW.

Tnx guys! Really helpfull! @BM, so you found the hidden question.;)