As for BYOB, nope, not allowed.
Howard has been known to take the odd bottle of Ch‰teau d'Yquem onboard SQ[;)]
Yes, I've BYO'd on VS, SQ and AA.
The written rules vary slightly between regulators and airlines, and sometimes it's that the pax may only consume alcohol served by the crew.
However, the reality is that it's a tricky one, and on the occasions I've done it I've always deliberately sent a very clear message that I completely understand and will respect a 'No', although I've yet to be refused.
On AA, the FA had to ask the Captain, who happened to be a wine lover and was delighted someone had brought on board a 1990 Yquem. On the return flight coincidentally I had the same cabin crew and before I'd even sat down they asked me if I needed any wine preparing, at which point I exposed a 1997 Pichon Baron that they looked after for me.
On VS, the FA asked up the chain, and then provided me with a corkscrew to open it myself.
On SQ, there's no fuss at all.
Since the liquid ban, I've only BYO'd dessert wines bought in duty free where carriers don't provide it themselves.
With the advent of more and more screw tops, I can see a time heppening very soon where there won't be a need to have a corkscrew on board particularly in J.
I also recommend only half bottles, where it sends a message of moderation.
13 Dec 2003 AA FC LGW-RDU Chateau d'Yquem 1990

14 Dec 2003 AA FC RDU-LGW Chateau Pichon Longueville Baron 1997

8 Oct 2004 VS UC LHR-IAD Chateau Suduiraut 1997

18 Mar 2008 SQ R LHR-SIN Peller oak aged icewine

H
[edited to correct typo]