Breezy_Pete

You may or may not get the alternator start up correctly if the blue wire is broken. Unreliable is the word.
I believe it is not the blue one that causes the ASR light to come on, it's the other one, which I wouldn't mind betting you'll also find is broken.  Fix (only) the blue one first, and see if the ASR light starts behaving, if you really want to be scientific about it. I suspect you'll find that doing just the blue wire will fix your battery charging problem, the battery light will now come on with ignition, but your ASR light will still misbehave.

Both those numbers are on the page I linked.  Look around the item numbers 47/48 area.  Call your local dealership/TPS for prices, or email the helpful Mike Hindle via [email protected] for a quote. Don't forget to include your registration number or VIN.

This fuse may also power two other devices, one of which is faulty.
The first, and most likely, I think, to be causing your trouble is "N79 Heating resistor for crankcase ventilation". Not sure exactly where this is on your engine but possibly in a breather module on the rear of the engine block?

 
The other device is oil level/temperature sensor in the sump (if fitted on your car).
 
Unplug both, fit new fuse, then plug in one after the other observing which causes the fuse to blow (when ignition is switched on).

Added after manufacture by a previous owner, no doubt, for some extra widget or other.
 
As you say, only a brown one on the negative clamp according to the wiring diagrams.  That is for voltage sensing, along with a red/yellow one from fuse 10 on the battery fuseholder go to the Onboard Supply Control Unit in the cabin. It's in charge of the electrics, so needs a 'pure' view of the battery voltage unaffected by the current flows that might exist in non-dedicated wiring.

Something to do with windscreen mounting.
Google worked for me. Third character is a zero, not a letter.

6Q0 945 511
 

1. Probably similar if not exactly the same
2. You may have to remove some underbody plastic trims to find it.  Info on erWin suggests that connections for both pre-and post-cat sensors are in the same box, but location not specified.
3. Z19 is the heater element within the precat sensor. G39 is the separately named sensing element itself. Both in the same part, in other words.
4. In the relevant erWin document.
5. If there was a specific problem with the heater or the supply to it, you would have a fault code that referenced it, I believe, hence Tech1e's earlier comment "Looking at the fault code it's not an electrical issue as such"
6. They mean the car side of the connector pair where the sensor plugs in. As opposed to the half of the connector that goes to the sensor.
 
"I don't wish to make a user account, then use my card account number on online sites, because you can never be too careful"  Then you won't have access to this excellent resource of information.  Seriously, you buy nothing online with a credit card? I'd consider that quite a bit too careful.

Correct.

Yours is behaving normally.

I have good news for your cousin. This is almost certainly just a cracked strip-fuse, replacement of which will restore full ABS function. The fuse in question is in the fusebox on top of the battery.
See here. (The good news starts at post #6)
A/C probably just low in refrigerant.
For the low voltage faults check the signal wires to the alternator. They often break near the gearbox.

No oil should be getting up to the engine cover/airbox, so maybe a first step is to take that off and look at how much oil - if any-  there is inside where the air filter goes. Anything that is in there must have come from the PCV fresh-air hose, I think. If there is evidence of oil in that hose, and up in the air filter housing, it would suggest that the crankcase pressure is much higher than it should be, which may point to blockage of the convoluted hose from PCV valve to inlet manifold, or within the valve, or within the manifold passage that the plastic hose connects to. 
 
The PCV valve can be taken apart, if you're careful, to inspect the insides. There are three or four 'ramp' type catches that can be undone around the circumference, then the lid comes off. I can't  remember how the plastic hose disconnects from the inlet manifold, but I think it's easy enough. Where yours has sealant between the PCV valve and the chain cover, there should be an o-ring, so that should be removable/replaceable if the sealant isn't too strong. 
 
You don't actually mention how the engine runs? Is it performing OK?

Part number is N 10424903 if that helps.       
TPS or Skoda dealer should be able to help. Good motor factor ought to be able to cross-reference that part number to something generic they have that fits.
Bit of earth wire out of twin 'n' earth wrapped under the nuts as a very temporary fix...
 
The OP subsequently discovered that putting "VW strip fuse" as a search term into ebay brings up quite a good selection of results. (Better than just the above PN).

Starter solenoid wire almost broken, but not quite. I reckon.

I believe that is the right part number for the overall housing/thermostat/temperature sensor, yes.  Comes with O-rings for mounting against engine head and for temperature sensor which will be already mounted.

Or with suffix F (6Y2959565F) if the car has electric windows.

This any good?

Hi Tony, and welcome.
Have you visited this thread? I guess it has the answer(s).

30mm 12-point according to these guys.  That's if what you have fitted is N 90654502 as defined here (which it should be). Also assumes that Concept-1 are selling a nut that's the same as the genuine one...

Just came across this thread and see that I didn't close it out when I found the real fault a week later.
 
Turns out it was all down to a water leak. Any time I said it was fixed, above ^ was purely down to the water having evaporated away.
The rear light cluster seal on the nearside was letting in water (they washed the car after the work at VW). The leak path is directly above a 5 or 6 way vertically-orientated un-waterproofed connector, the lowest two ways of which are 0V and indicator.  So while there was water between these two pins, any activation of that indicator would instantly blow the fuse and put everything out.
 
On the offside, the pins are in a different order, and that side showed no evidence of having leaked.
 
A bit of closed-cell self-adhesive foam was a five minute fix once I'd discovered this.
 
Just in case it's useful to anyone else with a 9N Polo, who might come across this thread and curse me if I hadn't posted this last 'wrap-up'.
 
Picture shows the foam that leaked ringed in blue, some puddles inside the housing, and the pins that must have been getting connected by water:
 

^ Bang on, I think, but all three glowplugs will be the same, I'd think, so which one/two are being energised by each relay won't make a jot of difference.

Is it possible that it fits somewhere inside under where I've put the blue rectangle?
The rectangle in your loose part looks similar in size.
 

Have you checked the fuse above the battery?
http://www.briskoda.net/forums/topic/119972-00301-abs-return-flow-pump-v39/

And every other Mk1 Fabia model... it's a crap look-up. 
 
Standard rears on an 05 vRS are 232x9mm, see here, item 7.  VAG part number 1J0615601N

If you look at the layout picture in this thread, there's a handy colour (and size) key at the bottom.  5, 7.5 & 10A in mini-blades, 15, 20 & 25A in 'normal' blades.