Hi vw754,
I'm guessing this is a Q7 not an A3 TDI? If so:
1. It sounds like your battery has had it I'm afraid, either that or you have a slight long term current drain, but the former is more likely. You should not try to remove the battery to charge it, instead you should use the battery charge/boosting terminals under the bonnet. They are located to the right as you stand in front of the car looking under the bonnet. The live has a red cap with a + mark which you need to flip back, the earth is a plain terminal located close by. The battery is located under the passengers seat so it is a pain to get to. It is also advantageous to charge the battery 'in situ' as it allows the energy management to monitor the current absorbed by the battery from your charger and thus recognise the charge state of the battery.
2. Your right, it is not normal. It sounds like the tailgate lock motor has just about had it. Is it closing OK? Is it an electrically operated bot lid?
3. You will find the tyre pressures on either the edge of the drivers door, the inside of the lower B-pillar with the drivers door open or the inside of the fuel flap, depending on the production date of your car. Although, they sound like unusual size tyres to me, are they aftermarket wheels?
4. The brake fluid reservoir is located on top of the master cylinder. Open the bonnet and you will find a flap on the drivers side on the black trim that runs the width of the car between the bulkhead and the bottom edge of the windscreen. The fluid reservoir is under here.
Tech