Randomly blowing white smoke and running rough.

[93_Clubman]

Idling a bit faster than usual, but don't believe that's HLA noise - certainly no FI guru here, but reckon it sounds more like a leak on the exhaust/turbo manifold side of things.

[speed]

Ok, just s couple of thing's..
The filter you're running of the crankcase vent is a no no.
Wipe your finger under it and tell me you don't end up with oil on your finger?
Should run a hose from there to just behind you air filter yet pre turbo.
Re the blackness on the heat shield, is that just burnt paint or some oil staining?
The duct for the cold air feed looks cool, except the part that it's not clamped to the air filter, at least that's how it looks on the photo. If not clamped, you still allow hot engine bay air in the filter.
Silicon elbows can suck into themselves under extreme pressure reducing performance. Better with metal bends ;)
Re cleaning the HLAs, don't bother. Even if that is the cause of ticking, it will come back soon thereafter. Don't think it will stop any smoke either.
Definitely use lifter free as 93 clubman suggested.
Smoke on start up could be valve stem seals meaning need new ones, can't clean or repair those

Will watch your video when I get home

[speed]

There is a fair bit of engine movement when you manually move the throttle. Broken engine mount?
Sounds low on oil too. Back to thinking cracked piston or fcuked ring.
Would have been good to hear on the exhaust side, to see if it was louder but if exhaust manifold, I'd suspect you'd see the smoke in the bay.
I'd be checking compression again. If fine remove the exhaust manifold or turbo and tape paper towel or something to it and give it a rev then stop the car immediately. If the towel is oily, you have an issue in your engine, suspect combustion chamber.
Anything on top of this from me is a wild guess.