You're overreacting. 2 x 0.75 mm2 or 3 x 0.75 mm2 is absolutely sufficient for 10 A.
In my shed I have a 2 kW heater on 230 V, and the cable doesn't even begin to get warm.
Heater cable will have a higher current rating, because the insulation will be rated to a higher temperature. If it doesn't feel warm, it's because the duty cycle is low. My parents have an immersion heater in their house, for when the gas boiler fails. It has a 230V 3kW element and 1.5mm
2 cable which does get fairly warm when it's been running for a long time.
I know. If anything the current rating is less for flexible cords on potable appliances, than for installations because even if the insulation can withstand higher temperatures, the cable will be too hot to handle.
It's opposite. Residential installations require higher cross section.
If the cable is buried in a wall, as is often the case in a fixed installation, then yes, it will need a larger cross-sectional area than a free cable.
More often than not the minimum cross-sectional area is determined by the voltage drop, ensuring the breaker trips quickly due to a fault and preventing the voltage on the earth conductor from reaching hazardous levels, due to faults, rather than the cable heating up.
I researched a bit and it seems that 3x0.75 cables are usually rated for 6A, however some occasionally say 10A.
Yes, that's fairly standard.
Also by the logic that 1.5 mm2 cables are usually rated for 16A, 0.75 mm2 should be good for at least 8A (1.5/2=0.75) instead of 6A .
No, because it doesn't scale linearly.