forgot the heater problem, again my golf had this one too...
if you tace the water pipes round the engine you will see two heading off into the bulkhead. Just before they go through the bulkhead (towards the heater matrix) they should both pass through a valve (one valve on each pipe). On the inlet side this valve is metal and on the return side it is plastic, in between the two valves there is also a thermo-controlled bypass for the heater matrix.
All the valves do is control the flow through the matrix to prevent it exploding when the engine is running hot (apparently this was a problem in early golfs and warranted a recall).
Your problem is probly with the metal valve, take it out and test it by running water through it (in the direction of the marked arrows), cold water should run freely through the unit.
If faulty a replacement will be hard to find at a scrap yard, it took me 4 tries, the other three had the same fault.
Good luck