I did some more tests, and it seems that the pops occur after I play the first adpcm wav. If I am playing another mp3 or adpcm after a adpcm, I can hear pops at beginning of the sound. First mp3 OR adpcm ever played is fine !
The clics actualy very much look like the startup clics I have if I am doing an hard reset with Adafruit_VS1053::reset(). Or when I power on everything.
(something like the breakout board output caps charging maybe ?)
So it seems that -something- (in the codec state ?) is left in a -certain- state after I play one adpcm. And maybe makes the chip reset or something if I am playing something else after. Maybe this is just the VS1053B crashing...
And -houraah- a simple Adafruit_VS1053::softReset() just before the Adafruit_VS1053_FilePlayer::playFullFile() solves the problem without any noise !!!
Thanks for the follow-up.