Rear speakers in A3 buzzing??

You need to rewire the rear speakers to the HU. It's not the speakers at fault but the puny Audi amp driving them. The amp is inside the tupperware sub enclosure in the cubbyhole in the boot and also drives the sub, it's a piece of garbage (see below) as is the wiring to it and will always be likely to induce alternator whine & interference due to lack of proper screening. Plus it's only 2 x 20w whereas the Alpine will be kicking out at least 2-3 times that power so keeping it just gives you a total imbalance between fronts and rears.

Yes that's right, "although disconnect the rear speakers from the HU" should read disconnect the rear feed to the rear amp, you can then reconnect the feed to the sub pre-out on the HU and then jack the sub level up in an attempt to provide some bass.
You can connect the new wires directly to the speakers or if you don't mind losing the sub then you can pick up the feed to the rears from the sub connector which saves pulling the rear panels off.

When you say you found the amp in the boot, do you mean the one inside the sub enclosure as shown above?
The connector should be a red one like this:

The HU will have it's own loom, you need to trace this back to the Audi loom which is most likely stuffed down the back somewhere to make room for the wiring.
Somewhere behind the dash will be 3 connectors:
Black power ISO - standard ISO plug providing power to the HU
Brown speaker ISO - only 4 wires on this as it just feeds the front speaker outs from the HU to the front speakers.
20 pin mini ISO - long thin connector either black or multi coloured (yellow/blue/green)
This is the feed to the rear/sub amp and should in theory be either plugged into a red adapter which then connects to the rear RCA's on the Alpine or a big chunky line out converter (usually covered in foam) which will then be plugged into the rear speaker output on the Alpine. There are 2 different ways to feed the rear amp from an aftermarket HU, via the pre-outs or via the speaker output, so it'll be one of the above. Just pull all the wiring out and remove the glovebox if you have to as this makes feeding all the wires in/out a lot easier otherwise it's easy to pull the wires from their connectors if they get caught on something.
Can't really recommend what to do until you have confirmed how it is wired up at the moment, post some pics of the wiring would be really useful.

Can't actually see where the feed to the rear amp is coming from. This is the adapter that takes the feed to the rear amp:

There should be 4 wires going into it left signal, right signal, signal screen and a remote on 12v trigger to switch the amp on when the HU is on.
You have no RCA's connected at all, so they must have used a hi-lo converter on the rear speaker outputs which is why you're getting buzzing, but from the picture it almost looks like they just wired the speakers directly into the rear amp, which you cannot do as the signal is way too powerful.
Can you trace those wires back and see where they go?
The red adapter plugged into the blue/green/yellow Audi plug should have RCA sockets on the end, which should then be plugged into the rear RCA output on the back of the HU. Then there will be a single blue flying lead which connects to the power antenna lead on the HU to provide the 12v trigger to turn the amp on.

Think i can help here. What you need is one of these

Your HU should be capable of generating the needed 1.21 gigawatts of electricity to get it going. Just be sure to stay below 88 miles per hour...

and you'll need to wire it directly to the battery otherwise you'll keep blowing fuses!