While laying down a track in pattern mode with the intro on Section A, Track 1, the drums and bass on Section B, Track 2 & 3 and a Legatto Trumpet on Track 4. I recorded the Trumpet using the Assignable 1 function switch, which gives a total different sound than without. How do I bring that effect in my mix, so that I don't have to turn the Assignable 1 function switch on all the time?

Either record yourself turning the [AF1] switch from Off to On; or INSERT a Control Change (cc86) message at measure 001: beat 1: clock 000
cc086 = 127
The Assignable Function 1/2 buttons are cc86 and 87, respectively. Controller changes must be documented into the track event list - as you might imagine each controller has a default start condition. If you wish to affect a change to that default start condition you must record (document) that change of status.

From PATTERN mode select the Track with the trumpet data
Press [EDIT] to view the Event List for the trumpet Track
Press [F5] INSERT
Set the Event Type = Control Change
Insert cc086 value 127 at the downbeat of the first measure. This will activate the [AF1] function when the track is played back.
At 001:1:000 set the CTRL NO = 086, DATA = 127
Press [F6] SET to enter the Event

The Assignable Function 1 and 2 buttons, like all Control Change devices default to either a minimum/maximum or neutral position when a Program is recalled. So for example, when you initially recall a PATTERN:
MW (cc001) resets to 0 minimum
BC (cc002) resets to 127 maximum
FC2 (cc004) Foot Control resets to 127 maximum
FC1 (cc011) Expression resets to 127 maximum
AS1/2 (cc016/017) reset to 0 center
RB (cc022) resets to 0 center
SUSTAIN (cc064) resets to 0 minimum
SOSTENUTO (cc066) resets to 0 minimum
AF1/2 (cc086/087) reset to 0 minimum
FS (cc088) resets to 0 minimum
PB resets to +0000 center
Aftertouch resets to 0 minimum

If you want a different value initially, you must record it to the Event List. Think of the AF1 button like you do the Sustain pedal, it is initially in the OFF position, in order to start a section with sustain pedal active the first recorded event must be cc064 ON (value 64-127). You cannot start recording with your foot already on the sustain pedal, you actually must record the On event and document it in the track data. MIDI data is not audio, so the events cause a response in sequential order. So by placing an ON value for cc086 at the top of the Section will ensure the Articulation that you desire.

The AF1 will remain lit (and that Articulation, legato, in the case of the Trumpet Voice) will remain until a cc086 = 0 message is received or you Change Programs and a Controller Reset message is received.

Thank you so very much Phil. It worked just like I envisioned it. There's just so much to learn about the Motif and I'm grateful you are there to share your knowledge of it!