Extraordinary Abilities were non-magical magic. They allowed you to break the laws of physics, which means that they are pretty supernatural in origin, despite the game rule saying that they are not.
No. The game rules specifically give those metals their abilities and provide reasons for them to be in the game. The game rules provide no reason at all for halflings to be as strong as a half-orc.
Hm... but both of your statements are interpretations of the written text. EX break "the laws of physics" (which I read as "our laws of physics and our known limits of RL earth biology"), yes. This is RAW. But this is not "supernatural" in the game definition of the word supernatural. It is super-natural compared to our RL "nature".
Halfling strength is not marked as EX, no. But neither is orc strength. Or Darkvision. Or most other non-use racial features. And you'd have to agree that especially Darkvision is somehow super-natural as it doesn't exist in our world. Not in the way it works in D&D at least. It is not explained though. Orcs just have it. For unknown reasons. (I guess a nod to Tolkien)
The game rules also give halflings their attributes. They neither discuss the physical properties of adamant (which would be interesting for me as a chemist

Well, I am differentiating between Adamant(ine) in D&D and what was called Adamant (or adamas) in RL. Every really hard material was called adamas in ancient Greece. This included "proto-steel", corundum and diamond (though it is unknown whether ancient people would differentiate between corund and diamond even if diamond is one Mohs score ahead of the corund.). These materials were considered unbreakable (=adamas), even if we know that they are not.
Some say that medieval alchemists later used "Adamant" (which is probably why there is the english attribute "adamant" in the first place) as a name for really hard (and maybe unobtainable, mythical) minerals. Tolkien uses Adamant as a really hard gemstone as well.
In D&D, adamant(ine) (when its properties are described more detailed) is a metal. D&D regularly uses steel, so these two are not the same (in contrast to ancient Greece). This is logical, as cutting a gemstone in a way that it can be worn as full plate armor would be quite a task (yeah, I have seen diamond armor in some JRPGs, but... eh...). For 5e, there is a few months old thread in these forums where adamant is being discussed http://www.enworld.org/forum/showthread.php?517756-Is-adamantine-a-metal