Max - ok let's try to get to the bottom of this.
your airbrush is new so the teflon washer probably isn't the culprit.
Your needle/nozzle combo is new at least for the medium so it's probably not that...
Your compressor appears to have a tank already so that should dampen any pulsating from there...
Ok - when you put the needle in gently push it all the way forward until it is tight in the tip (i.e. can go no further) then tighten down the knob at the back of the brush that holds the needle in.
Check your spray bottle to make sure the tiny hole that allows air in the bottle is clean and clear... if you don't see the hole look closer, you can poke the dried paint out with a toothpick or straight pin.
Make sure the head is screwed hand tight, turn it as tight as you can with your fingers but don't try to force it too tight...
and no pliers
Disconnect the hose from your airbrush and turn the pressure up gradually, see if the air coming from the hose pulses. If not we can totally rule out the compressor.
Hopefully we can come to something with all this!
Good luck!!