Plumback basically means it is 'plumbing' (piping) the pressure build up from the turbo back into the system. The HKS (guessing you have the SSQV) is an atmospheric BOV which is the opposite of plumback, so instead of it keeping the pressure buildup within the system it vents it out making the BOV noise. Atmospheric BOVs cause all sorts of stalling problems and may be part of the cause of your starting problems. Even though they sound pretty dam cool (i always wanted one ) some people actually say they lower performance because the car has to build up the pressure after each gear change and bov vent. So try changing back to the stock or any other plumback system, can propably even plumback the SSQV so maybe look into that. Should be able to pickup a stock R33 BOV for under $50 on forums, just search around.
As for oil, if it is 20Wsomething then i'd bet some money on it being the cause of the starting problems. Its winter now and the mornings are cold so you add that onto the thick oil and its going to be tough for your car to start and would also explain why the problems disappear when the car is at operating temp. Try changing to some thinner oil (10W40) or even 0W40 and run it in for a while, post back here once you've tested those 2 things out and see how you go. Check out the 'goods on oil' thread for some more info on what oils are good.