You are of course right. It is 230 V * sqrt(3) ~ 400 V. I don't know how I came up with the 360 V. I don't use these values very often so they are not really imprinted well in my memory. The point stays the same, although circuit breakers rated close to that value are actually commercially available so we're not that far away I think.

That's just a technical issue though. A kettle with a resistive heating element running through the whole body of water you would not even create that high of a temperature. Think about it as several standard kettles connected in parallel.

I'm not sure if vacuum pumps are exactly cheaper and more efficient at making water boil (evaporate in full volume instead of just surface) but it would be quite pointless. It's not the vapour bubbles that cook your pasta or brew your tea, it's the water temperature. That's why Papin's pressure pot is a thing, the high pressure increases the temperature limit and allows you to cook watery food at temperatures above 100°C.

It's called induction cooker.

Physicist here. To boil 1 litre of water you need 4200 J of energy per degree of Celsius. So to heat water to boiling temperature from room temperature, you need approximately 4200 J/°C * 80°C = 336 kJ of energy. To deliver that amount of energy in 5 seconds means you need to supply power of 336 kJ / 5s = 67.2 kW. With standard 230 V outlet this would be 67.2 kW / 230 V = 290 A of electric current. Using 3phase plug for 360 V would require 186 A. Cables in walls are typically rated for a few tens of Amperes, definitely not hundreds. This is why circuit breakers are typically rated for ~20A. Running such a high current through the cables would literally melt them.

TLDR: You most definitely can have a 5-second kettle but it would set your house on fire.

EDIT: Electric vehicle superchargers are usually rated for 50-100kW, so you could make a kettle that plugs in EV supercharger and boils water in less than 5 seconds.