Leak won't be related to the thermostat really - lots of them leak here. Remove the plug and clean it up and pop it back in - don't over-tighten it as the thread will strip easily. A copper washer or rubber O ring can help improve the seal.

Flow of hot water the heater matrix is not controlled by the thermostat or the heater controls - as soon as the engine starts warming up it transfers heat to the water in the cylinder block which is continuously pumped through the heater matrix. It is designed like this to get hot air quickly to demist the screen. The temp control knob just operates a flap controlling the amount of hot air from the heater matrix that can enter the car.

All the thermostat does is control the flow of water to the radiator - until the water reaches 98 deg C it stays shut. This maintains the engine at optimum operating temp. The sensors you refer to are for the water temp gauge on the dash and sending a signal to the ECU to control mixture settings. There is a temp sensor in the cylinder head too sending data to the ECU. Clever stuff - until it goes wrong!

You should find the Duratec warms up quickly, even on light throttle openings - 2 miles of normal driving should get the needle to the centre of the range on the temp gauge.