I do apologise, I've searched until my brain has literally melted out of my head but can't seem to find a definitive answer:

If I have the engine off and the ignition and AC on, should the radiator fan(s) in the engine bay be spinning? As mine aren't.

I know they 'work', as with the engine idling they come off and on intermittently, regardless of the AC being on/off, but don't spin constantly.

If it's meant to be spinning with ignition and AC on but engine off, then should I be thinking a fan controller issue? I've checked the fuses on the battery and they're fine, do I need to check a specific one in the fuse box too?

The car doesn't seem to like hot weather much and although the AC gets cold, it's not Arctic - and definitely works a lot better when at speed (or with colder ambient temps, weirdly). Which is how I got to checking the fans and also why I'm assuming the AC compressor is fine.

I've got no dash lights or weird behaviour otherwise, and don't really want to pay for reading the fault codes unless I'm sure something is up.

Again; I'm a mechanically challenged doofus, so apologies if I've simply got the wrong end of the stick or chasing shadows here.

I have a copy of VCDS so would check fault codes for free, if you want. If the Fabia is the same as Golf/Leons etc then it probably won't show a fault anyway. With them, if the AC is on, the fans should be spinning at slow speed all the time. If they go intermittently between off/full speed, then it means the resistor to provide the low speed fan current has burned out in the fan controller. I'm guessing the Fabia is the same, but my AC doesn't work so I've never really checked the behaviour.

edit - just noticed that you said with the engine off, I don't think the AC system runs with the engine off as it's belt-driven from the auxiliary belt? If you're trying to isolate fan controller behaviour, I'd check what the fans are doing with the engine on and AC on.

Cheers. With the engine on, the radiator fans go from on to off in their own random rhythm, but definitely not on constantly. There doesn't seem to be any difference between with the AC on or off that I can see? This is why I'm all very confused.

Yeah, if they're switching between off and full speed with engine on and AC on, that sounds very much like the fan controller failure that plagued the Mk4 Golf platform (http://www.nime.co.uk/content.php?mk4fans). I believe off/full behaviour is normal for when the AC is switched off anyway, but when the AC is on then they should be on slow constantly, and only ramping up to full when it's actually required.

Arse.

Am I right in thinking the controller is part of the fan assembly and I'll need to replace the fans too?

Hmm, I don't think so. I thought it was a separate module under the battery tray that could be removed and then repaired (or upgraded with one of the Nime boxes from my link above). Mine didn't fail though, so I'm not 100% sure.