a. Is it possible to change the performance's time signature from 4/4 to let's say 9/8? I ask this, because I create a 2 6/8 bar arpeggio on pattern mode and then on the performance, when I assign this arpeggio it is interrupted on the 4/4s and doesn't play as 9/8.

A phrase which is two measure of 6/8 will never play back as 9/8, the math does not work.

Record phrase to the sequencer in 9/8 time, then when you convert it to an arpeggio, your phrase will playback in 9/8. You cannot change the time signature if something recorded in 6/8 to anything but 6/8.

b. Is it possible to transpose the whole performance?

Yes, it is. If you mean you want to press certain keys on the keyboard and have them sound in a different musical Key... Then yes.

Each Part of the Performance has a NOTE SHIFT parameter (do not shift the drums/percussion).
Press [EDIT]
Press the Part number 1-4
Press [F4] TONE
Press [SF1] TUNE
NOTE SHIFT is by semitones
Shift as necessary, all but the drums.

What do you want to happen?

Ok, I made a typo earlier. It's not 6/8 it's 9/8.
What I do is I record drums on a pattern (which is 9/8) a 2 bar 9/8 arpeggio.
I extract the track with the 2 (9/8) bars recorded arpeggio to a user arpeggio.
When I assign this arpeggio to a drum voice part of a performance, it doesn't play trough the end (9 eights) it plays 8 eights, as if the time signature of the performance is 4/4s.
This is what I mean.

Ok found the problem:
When I exported the phrase from the pattern to a user arpeggio, I exported only the 1st measure, from meas 001 to meas 002. When I tried with meas 001 to meas 003 everything was ok. Both meaures where exported.
Thanks again for the help and I am sorry for spending your time for such a silly problem.
Happy holidays!!!