What age is this car?

Are you recalling the Nikasil saga? That was a long time ago!

OP - without more information it's random speculation, but If it's not leaking out, it's being burnt.

How is another question. You won't necessarily see smoke, and the cat will tend to burn it off anyway (which won't do the cat any good and could ultimately kill it).

Generic answer is bore wear or valve stem oil seals.

Or maybe - I don't know BMWs, but I am told they typically employ a crankcase ventilation system that is intended to separate oil from the vapour and return it to the sump. If that clags up then it presumably goes into the inlet manifold instead, where the rest of the fumes go. Common fault I believe. Look up "BMW CVV".

Fixing the CVV, if implicated, won't fix worn bores or ineffective oil seals but it will improve the emissions which could be marginal - has it had a recent MoT?

If you have a compression tester then that would give you some info. I for one will never buy another old car without checking the compressions, after the last one!