Coolant Loss

Ok here goes the tale. I recently noticed that my 1996 Audi A4 110bhp TDI was loosing coolant fluid. On inspeciton I foudn that it seemed to be boiling off at the top hose to the radiator was too hot to touch, but the
radiator was cold. Having searched the net I replaced the expansion cap as a starting point but no change. These weekend I replaced the thermostat anf things have changed a little. Instead of the temperature gauge sticking like glue to 90degrees it now goes up when I accelerate hard but then after a while returns to 90. The radiator is hot across the top and this morning after a 60 mile run was warm in other places too. With the engine hot and running I have tried to hold shut the top line to the radiator after the T to the expansion tank in the hope of seeing water puped into tank to confirm water pump is working but to no avail. Should I go ahead and replace water pump of does anyone else have any bright ideas, for reference the system seems to hold pressure once the car has cooled down as when I open expansion tank it goes psss and level rises in tank, plus oil is black with no milky streaks.
Any ideas would be well and truly welcome.
PS Does anyone also know how to stop water accumulating in batery tray?

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