1) Is there any way set the Montage to both: MIDI and USB?

Yes. When the [UTILITY] > “Settings” > “MIDI I/O” is set so MIDI I/O = USB (green) your 5-pin MIDI jacks act as a MIDI Interface. The MONTAGE has a built-in MIDI (and Audio) Interface via USB. When connected to a computer (or host device) via USB, Port 1 addresses the internal MONTAGE Tone Generator on channel 1-16. Connect your external device to the MONTAGE MIDI OUT. It will be seen as “MONTAGE Port 3”, Channels 1-16.

This means any MIDI Track routed to “MONTAGE Port 1” will trigger the MONTAGE; any track routed to “MONTAGE Port 3” feeds the 5-pin MIDI Out jack on MONTAGE’s back panel.
Additionally, connect the MIDI OUT of your external device to the 5-pin MIDI IN on MONTAGE’s back panel, your DAW will see it as “MONTAGE Port 3” coming In.

2) When i switch back from "performance control" to "catogary search", the Montage forget the last choosen Bank/Favorite and goes back to "All".

This will be addressed in a future update.

3) When I start my DAW (Ableton Live, Windows 10, 64bit) and I start the Montage lateron, the DAW won´t recognise the Montage. So I have to restart the DAW.

Typical. When you launch most DAWs you may notice it surveys what is connected to your computer. A general good practice is to start MONTAGE (or any connected devices) BEFORE launching your DAW.

Some DAWs can rescan.... making a relaunch unnecessary. Check your DAW’s documentation for “rescan”, “refresh”... etc.

4) When I play an arpeggio sound, how can I change the tempo of the arp from 16th to 8 triplets for example?

Sorry question does not compute! Tempo is measured in “Beats per Minute”.
Perhaps you want to requantize the Arpeggio Phrase.

Call up the sound with the Arpeggio
Press [EDIT]
Press [PART SELECT x] where ‘x’ is the Part with the Arp
Touch “Common” in the lower left corner of the screen (blue)
Touch “Arpeggio” > “Common”

Set “Quantize Strength” = 100%
Set the “Arp/MS Grid” = 160 (eighth note triplet)

The Quantize Strength at 0% applies no change... and as you approach 100% you approach more strict 8th note triplets.