Is it normal to hear the noise of audio noise when pressing a key (init preset with the filter at 0)?
No filter does completely shut off the signal. At the lowest setting, the Filter cutoff is at 20Hz with the higher frequencies attenuated by 6/12/18/24dB per octave depending on the filter setting. So there’s still audio coming through, but at a rather low level. Or maybe you hear a filter click because of the Filter Envelope?
… or maybe you’re hearing the noise of the VCA letting the electronic life out.
Charming analogue 
It sounds like very soft pink noise, not a click, but like opening up a gate when pressing the key. Is that normal?
It the volume of the said noise follows the amp envelope, then I would say it is the electronics behind the VCA.
I’ve already heard that. It’s analogue, mate, it’s alive. Plus it won’t be noticeable when your oscillators are on (or will it?..). Don’t worry, play music
Thanks I was worried that something may have happened during shipment, because the box arrived with some damage.