So your friend, looked at the outside of the motor and declared it to be good. WOW, He must have x-ray vision, or be all knowing! Stop listening to people who just have an opinion and look at the cold hard facts.
Start by pulling out the spark plugs and looking at them. Is the problem only on 1 cylinder or all of them. Are the plugs sooty (dull) black, oily (shiny) black, tan/brown, or have a white coating. Check the plugs after starting the car and running for 1 minute, 5 minutes and a long drive. Take notes or pictures and compare.
1. Your engine DOES smoke when starting, thats a fact you can see every time to start it up. So what color (you already said its white)
2. As stated before in this thread, white smoke = steam, Blue = oil, Black = rich. So you have water or oil in the combustion chambers when the engine starts.
3. If Your engine is leaking water/coolant into the combustion chambers from the cooling system. It can't leak in from anywhere else, since that's the only water in your car. when driving the car, the radiator is pressurized to about 12 psi (look at your cap), but the combustion chambers get pressurized to about 100-200 psi. The pressure keeps the water out. But when you turn the engine off, the water is still boiling hot and the 12 psi forces a little water into the combustion chambers. Then when you start up the water has to burn off, but the combustion chambers are cold and so it takes a little bit to burn off (heat up).
4. OK, we'll take a flyer and say its not leaking, depending on where you live, there might be some condensation happening inside your intake which is getting sucked in when you start up, but unless its a lot of water, it would burn through pretty fast.
5. If #4 is true, you would never have to top off your radiator, If #3 is true, you will be periodically filling up the radiator or the radiator fill bottle.
6. So if #4 is true, park your car in a dry garage for a few days and see if the problem goes away. Then don't worry about it. If its #3, its either head gasket or intake manifold, or you have a cracked head (not likely as you would see more water loss).
7. If your engine burns oil all the time, you'll be adding oil all the time to keep it at the mark (dipstick).
8. Similarly the oil pressure is about 60 psi and when the engine is running the combustion chamber pressure is greater than the oil pressure and keeps the leak slowed.
9. Most oil burning during running is either due to bad valve guides or bad rings. You can check for bad rings by checking compression on each cylinder. Bad valve guides tend to leak a bit of oil down them, because it gets suck in from the top of the head (by the vacuum in the intake). 1 oily plug out of 4 or 6 would indicate you have a problem in only 1 cylinder and probably have a head leak.
Write down what you have and be Sherlock Holmes, listen to the facts.