Correspondingly, when did Wolverine get his adamantium?
1999
Secondly, did Wolverine heal before adamantium? Yes. Even humans bones regenerate at a slow rate. So Wolverine, as a mutant with healing factor-- his bones would regenerate, but at a considerably fast rate. In the X-Men Origins: Wolverine movie, which you mentioned, he had his bone claws broken by Sabertooth before he had adamantium placed on his skeleton.
Hereof, why did they put Adamantium in Wolverine?
Wolverine possesses Regenerative Healing powers. During his exposure to Adamantium whilst having it bonded to his skeleton, his DNA was manipulated into seeing the Beta-Adamantium as his Skeleton. He can regenerate his Skeleton very quickly, but the Adamantium takes time to grow back.
Are Wolverine's bones coated in adamantium?
Wolverine's skeleton is coated in the indestructible metal adamantium, and it makes him nearly invincible. Wolverine also has superhuman strength because he has had to lug around an extra 100 pounds of metal for decades. And having indestructible bones means that Logan doesn't even need to use his claws to kill.