Sorry for the late reply as I was busy in some project. I did check your video and it seems like emitting little rich fuel (grey smoke). If it was a cold start, the fuel is always rich (13.6:1) instead of 14.7:1 as rich fuel provides better cold start of engine. Also I don't see any missing from the engine. I would like to have the video of coil when it produces the sound. There could be a problem with the ignition module/router causing load on the coil and it produces buzzing/humming sound.
Regarding EGR, it is just to control emissions by recirculating the exhaust gases into the intake for re-processing. When these cars were imported, they came without EGR in our region as the emission rules are not properly implemented. As long as PCV valve is concerned, it is embedded into the tappet cover. You must have observed a hose connected to the tappet cover that is going to the air filter box, it is actually connected to the PCV valve. If you think the PCV is faulty, replace the cover with another one to see if the problem gets resolved.