Electrical – Figuring out the correct way to connect a duct fan (europe)

Matching colors is usually correct, but there are exceptions. While this is considered the "right" way, it is for safety issues. The light will work either way. But we don't want the power from the brown going down the blue usually neutral in random parts of the wiring.

Which is why turning off the circuit with the switch is usually safe. If the wiring was reversed, with the switch on the blue neutral, the light will still work, but you would have gotten a really nasty full mains shock, instead of the "little" attenuated by dimmer shock. Always kill power to circuits at the breaker before working on them!

Dimmers, when full off, should indeed be full off. The fact it illuminates a light means it is defective. It needs to be replaced. It's not unusual for dimmers to emit a slight 50 hz hum during use, the volume proportional to the current being passed. But they must be able to completely open the circuit.

If you do get another dimmer instead of a regular switch, do ensure the lamps in the fixture are dimmable, and the dimmer is compatible with the lamp type.

TL;DR: Whoever installed your ceiling fan had some terminal screws loose

The good news is that the green wire is unmistakably tagged as an equipment grounding conductor, and was likely not the current return path in the original wiring configuration. The bad news is that whoever originally wired this did a hack job, deciding to use some blue wire they had left over from the last hack job as a neutral wire (grounded conductor), which grossly violates NEC 200.6(A):

200.6 Means of Identifying Grounded Conductors.

(A) Sizes 6 AWG or Smaller. An insulated grounded conductor of 6 AWG or smaller shall be identified by one of the following means:

(1) A continuous white outer finish.

(2) A continuous gray outer finish.

(3) Three continuous white or gray stripes along the conductor's entire length on other than green insulation.

Now that that facepalm moment is out of the way, it's possible to fix this by nutting the blue and black conductors from the fan to the black wire from the ceiling, and the white wire from the fan to the blue wire from the ceiling. While you're up there, please, please, please tag the blue wire from the ceiling with a piece of white electrical tape -- there's no way to bring the current situation fully up to Code without ripping out the offending neutral wire and replacing it with a white or grey wire, but a tag will at least keep the next electrician's eyeballs from frying when he or she stares at your ceiling fan's wiring.