Concert 2 to aftermarket HU (A4 2001)

Yes that's a Fakra connection, which is strange to have on an 01 model, you'll need an adapter to take it to ISO, this part number CT27AA45:
http://www.nexxia.co.uk/Car_Stereo_fitting_kits/antenna_adaptors.htm

Also the PC9-401 adapter uses your speaker outputs and a line out converter to feed the rear/sub amp. You'd be better off with the PC9-404 which uses the rear RCA's. On the brown front speaker connector you'll see 2 skinny wires bridged between the left & right speaker connections. This is the feed to the centre dash speaker. I suggest you cut one of them to disconnect the entre speaker as it's a hideous piece of crap tuned to the frequency of a baby crying so you really don't want it in your system.
You will find the rears and sub are very quiet compared to the fronts because you will now have at least twice the power going to the fronts than the stock HU so the feeble 2 x 20w rear amp will struggle to keep up. I would rewire the rears directly to the HU and use the adapter just for the sub, or just fade to rear.
The other problem is ignition on. Your new HU requires a permanent live to retain settings and a switched live to turn the HU on/off with the ignition. You won't have an ignition on live, just a perm live. So you either need to wire the ignition on to the perm live and turn the HU on/off manually or wire a switched live in.