getting white smoke with water

I would be getting a head check done, you need to prove that the head gasket is ok to start with, this is a quick and simple chemical test, most mechanics can do this in a few minutes.

How long has the engine been running?
Do you have coolant losses issues?

the engine has run 380 Kilometers after the overhaul and has gone through the 1st engine oil and filter change 250 kilometers. coolant loss is present but it leaks from one of the hoses over time, which is checked for every alternate days.

If the coolant losses is obnly due to the leak from the hose, get it rectified and retest. If water is dripping from the exhaust with no coolant losses, there is nothing to worry about. For an engine that is running correctly, there could be some water being dispelled from the exhaust, especially when the weather is cool.

It is actually too early to be changing the oil after the overhaul. Give the engine another 1,000 km to settle down and what grade of engine oil is being used?

currently i am using Caltex Havoline Formula Oil 15W-40. thanks for the answers to my queries, but what i am worried about is the excess smoke from the exhaust. recently i also noticed that the engine is reluctant to rev for a long time even with temperature at 50%. then after a long time of driving it becomes steady.also the engine pickup is kind a flat and not like before when pressing on the gas used to get instant response.

Ensure ignition timing is correct. If it is too retarded, the engine would not response too well under acceleration.

Depends on where you are located. Where I live, I would recommend 20W50 oil for the engine.