Wiring – Ceiling light not working, old wiring please advice thanks

The cable on the left runs to the switch. Power comes in from one of the two other cables via red, runs down the red of the switch cable to the switch. When the switch is closed, power runs back along the black and into the light via the brown. Goes thru the lamp into the blue, which connects to the common neutral black of the other two cables.

Switch legs can be confusing because the neutral coloured wire carries power back the the switched fixture. All is as it should be though.

Too bad I haven't updated answer when I rewired everything - but better late, then never, right? Here are the answers to my questions:

1. White wire is neutral in US in most cases... so it was in my case.
2. Basically, two whites were neutrals for two different circuits. I bought Voltage detector and separated right white wire by turning off circuit for lights - the other white still had electricity running through it so I was able to figure it which white/neutral I needed
3. Yeah, I just cut it, add in neutral connecting from the switch and then put cap on
4. For this you need Voltage Meter, there are quite few tutorials on YouTube that explain how to figure out which wire is which with Voltage Meter.