230V power
At 230 volts, a 16 A circuit carries 3,680 W and a 10 A circuit 2,300 W. Going the other way, a 3,000 W appliance draws 13 A, which is why 3 kW is the practical ceiling for a plug-in device on a standard socket.
How to work out 230 V loads
The 230 V nominal figure is itself a compromise. European harmonisation set 230 V with a tolerance of +10%/−6%, which covers historic 220 V and 240 V systems without anyone changing their transformers, so a UK socket often measures nearer 240 V and a continental one nearer 225. For power calculations the nominal figure is fine, but for anything sensitive to voltage, such as heater output or filament life, the local reality is worth measuring.
Questions
3,680 W at unity power factor. Continuous loads should stay below about 80% of that.
Harmonisation picked 230 V with a wide tolerance so existing 220 V and 240 V systems both comply without physical changes.
13.04 A at 230 V. That is exactly why the UK plug fuse tops out at 13 A.
Yes, typically between about 216 and 253 V within the permitted tolerance. Measure if it matters.
No. It is more dangerous per contact, but it needs half the current for the same power, which reduces fire risk in the wiring.