Can you overload a lighting circuit

There is nothing special about a lighting circuit in that sense - and there is nothing stopping you having a other loads on the lighting circuit - fans, window openers, TV amplifiers and alarms are often added to 'the lights' in small houses and flats, if it is convenient to do so. However, normally the breaker should be sized such that it trips at a level lower than that at which the cables would suffer damage (so not less than 1mm2 and a 6A or 10A breakers or not less than 1.5mm and not more than a16A breaker)

If the cable is undersized for the breaker, while unusual, this may be OK, so long as there is no risk of the load ever being increased, and the breaker is not soo big that it would not trip in a short circuit. Anything with sockets on (common for large buildings to allow whole fittings to be removed or re-located) should be designed assuming the load may change, and size the breaker and cable rating accordingly.

Yes you can have a 13A socket on your lighting circuit, but if you are daft enough to plug in a kettle instead of a small load, you can expect to be plunged into darkness, but not for the wiring to be damaged.

There is nothing special about a lighting circuit in that sense - and there is nothing stopping you having a other loads on the lighting circuit - fans, window openers, TV amplifiers and alarms are often added to 'the lights' in small houses and flats, if it is convenient to do so. However, normally the breaker should be sized such that it trips at a level lower than that at which the cables would suffer damage (so not less than 1mm2 and a 6A or 10A breakers or not less than 1.5mm and not more than a16A breaker)

If the cable is undersized for the breaker, while unusual, this may be OK, so long as there is no risk of the load ever being increased, and the breaker is not soo big that it would not trip in a short circuit. Anything with sockets on (common for large buildings to allow whole fittings to be removed or re-located) should be designed assuming the load may change, and size the breaker and cable rating accordingly.

Yes you can have a 13A socket on your lighting circuit, but if you are daft enough to plug in a kettle instead of a small load, you can expect to be plunged into darkness, but not for the wiring to be damaged.