All good info, but before you start replacing parts: your X holds either 7.5 or 8 liters, 3.0 IL 6 vs 4.4 V8. Your intial fill of ~6-6.5 liters was short/light to begin with. And, after ~9,000 KMs, yes nearly every E53 X on the planet will be down some oil, esp starting out a full liter short.
Don't feel bad: I have had 'short fills' done by US dealer(s), too...
When to check oil: after fully warmed up/driven, let sit for a few mins, (the engine will not drain down in a minute), and then check stick.
The "bit of smoke" from oil fill orifice is a bit of concern, but I would get a full oil fill and then note consumption, white tail pipe smoke, leaks, etc., if any.
There are pages of 'what oil to use' on this board and any BMW or car board; you seem to long past warranty, so any quality name brand full synthetic, either 5W-30 or 0W-40 is fine. 'What oil' is not your problem; proper fill is and then you can realistically track any symptoms of extraordinary consumption, but most Xs do burn some. Fwiw, BMW NA when pushed, will say that a quart per 1000 miles is fully within their 'tolerances'.
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