In my opinion, you have a gaulded piston, or broke ring. I would not run it, a rod through the block could result. White smoke is low compression and yes it is pumping oil.
I'd think you would have bad blow-by if rings or piston. If oil consumption and missing are related problem then I would think rings or piston. If separate problems you may be looking at bad injector for miss and turbo for oil use. With noticeable oil smell at idle I think you could detect bad turbo by removing air outlet tube and hold rag over outlet at idle. If it gets wet with oil I would suspect turbo. If you pull clean air intake from turbo and see any sign of blade rubbing housing you best replace it. Something tells me you have two different things going on if your blow-by isn't noticably bad. Good luck