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.
Portable lamps (at least in the US) are generally designed without a ground wire. The bodies of the lamps, even if metal, are designed not to be likely to be prone to a short to the hot lead. The standard lamp cord is therefore two wire (hot and neutral). Most modern lamps are polarized, meaning the cord/plug is designed to ensure that the hot lead is attached to the hot side of the outlet.
Sconces and other lamps that are intended for fixed mountings on electrical boxes have a hot lead, a neutral and a ground. The ground is the safety measure in case of a short.
When you convert a fixture intended for use with a ground wire to a plug-in setup, you need a grounded cord to preserve the safety factor. The simplest way may be to buy a grounded extension cord, cut off the socket end and splice the cord with the plug (male) end into your fixture.
Attach the hot lead to the black wire of the fixture, the neutral to the white (the neutral wire is attached to the larger blade of the plug and the casing is sometimes ridged), and the ground to the green (or bare).
You can then run the cord under a cord cover to a conventional grounded outlet.
P.S. Be sure to use a bushing or something similar to prevent any cord/cable from being pulled through and cut or frayed by metal edges at the point where it exits the fixture or metal cable cover.
CAUTION
This whole discussion assumes that you are installing this permanently (a wall fixture is not well protected at the back from damage or short) and on an interior wall. Exterior fixtures are specifically designed to attach in an exact way to exterior boxes to ensure that they are water resistant. Any compromise of that attachment mechanism may lead to leakage, shorts and danger of electrocution or fire.
Best Answer
The Europeans and the rest of the world are harmonizing on a color standard as follows:
According to trade deals with those nations, we must honor their color scheme for appliances from European providers. Our own scheme is:
The NEC allows light blue for neutral in certain cases, an obvious nod to our treaty obligations.
However... Anything you install must be listed. To be more precise, it must be a device approved by your AHJ (your local electrical inspector) and they simply rely on listings issued by UL, the main American testing lab.
Due to our treaty obligations, we must also honor listings to equivalent standards done by their testing labs such as CSA, TUV, etc. All these labs operate internationally so a German company might get UL listing for a fixture to be sold in the EU. CE is not a listing agency. RoHS is not a listing agency. Chinese suppliers are notorious for faking listings.