What would likely happen in terms of law in the UK and Commonwealth realms if it were discovered that Elizabeth or one of her ancestors along her line of sucession to the throne was illegitimate or swapped at birth without a legal adoption, or was a bald-faced impostor? If it were discovered, perhaps by DNA tests or something like that, that the man that eventually became known as King William IV was in fact a commoner’s child who was swapped at birth with the “real” future heir, would that result in over 100 years of laws and court rulings to be deemed null and void since they were done in the name of impostors to the throne and were never consented to by the real monarch (I understand that the Monarch is essentially a figurehead, but does, in theory, hold the source of legal power)? I’m sure someone must have thought of this before. I think I read somewhere that the coronation ceremony is just formality, and that the Monarch becomes the Monarch by operation of law according to the laws of succession.
You are correct that the coronation ceremony has no legal signficance; it is the succession laws that determine who is king or queen.
But they are laws, not objective realities. English law contains a presumption that the child of a married woman is the child of that woman’s husband. It may be the case that Queen Victoria, for example, is not the genetic descendant of George III. But at law she is presumed to be, and that legal presumption makes her, and her heirs, legally the kings and queens of the UK.
Nothing. It’s not as if the line of the monarchy to date has been terribly straightforward and lacking in intrigue. Parliament is sovereign anyway.
Do you honestly think there HAVEN’T been any bastards? If ALL of the British monarchs (or any European monarch, for that matter) were legit, I’ll eat St. Edward’s Crown. 
And even if something was found that meant that every law passed for the last 200 years was technically illegitimate, there would be a law passed by parliament about ten minutes later saying (in essence): “all laws passed for the last 200 years are deemed to have full force and efffect and are deemed always to have had full force and effect, despite [insert flaw here], so don’t go getting any funny ideas, so there”. Or something like that. In the broader sense, this is not uncommon: every now and then due to an error a piece of legislation is realised to have some sort of drafting flaw and this sort of corrective legislation is hastily passed.
Bastards can be a term of endearment down in Australia
Haven’t we already found that the rightful King of England lives in New South Wales?
Parliament says who is the rightful king, and who isn’t. Not genealogy.