"All land claims are backed by law."

Law is force.  If there is no force to back up a "law," it's completely imaginary.  Kinda like your "kingdom law" or your particular interpretation of "international law."  For example, in the Nuremberg Trials it was determined that aggressive war is the "supreme war crime."  Want to know how many powerful nations have ever been tried for war crimes under that standard?  Zero of course.   "International Law" is written by the powerful, for the powerful, and enforced by the powerful, to be used against their defeated enemies.  Welcome to international law 101.  

"States leaving? Heard of the Civil War?"

Yep, it settled the question of whether or not states may leave the Union.  Which part of that isn't sinking in for you?

"Falkland never had treaties with powerful nations of the time"

It wouldn't matter at all if they did.  It's a British possession because of the Royal Navy and no other reason.  You don't seem to understand much about politics.