> I haven't found anything in the Datasheet about the compatibility of functions of the pins, as each pin can be used for several functions.
In basically all cases, you can use one out of <n> possible functions.
I don't know the LPC54616J in detail, but if you need more ADC inputs, I would recommend another version with different pinout/more pins, or another MCU, or an external ADC.
> Does anyone know if the programming inputs, corresponding to pins 24 and 25 of the MCU, could be used to input analogue signals through them?
In theory, you can configure these pins as ADC inputs during startup.
But not only will you probably need jumpers (possible interference between programming and ADC functionality), but also lose debugging capabilitites. The JTAG/SWD is both programming and debugging interface. And forgoing the capability to debug hardly ever played out well.