Is it true that when extending a high watt appliance with a extension cord I should use a thicker (higher AMP) cable than the cable of the appliance?
Basically yes &mdash; as the extending cable should be the same or higher in capacity to limit the losses which get turned into heat.

It does depend on the distance &mdash; so it may be safer, more sensible and convenient to fit a new supply point where the device is to be used.

As for the sizes, the 3 * 1.5 is three cores or wires of 1.5mm2 in cross sectional area &mdash; most in industry just tend to say 1.5 or 2.5 and don’t mention the units as everybody knows... they should, of course, mention the units but ...

As for not finding extension cables that thick - they are obviously not common and are usually made specially as necessary - I have made a few in the past.