As for Thorin being buried with the Arkenstone, I've always interpreted this as being less about Thorin being able to have it through all eternity and more about acknowledging that it is better if NO ONE living has the Arkenstone; that it represents too much of a temptation not to be likely to start more squabbles in the future, that, given the bloodshed already caused, it is far better to put the thing out of everyone's reach.
As for Orchrist, why shouldn't he have been buried with it? It's his sword. He found it he claimed it. The fact it was made in Gondolin doesn't mean the Wood elves (who would be the only elves at the funeral, Elrond isn't there) have any claim to it, or that they accorded him any particular honor by not yanking it out of his cold dead fingers. It's never accounted as a royal treasure, so it's not like Dain has any claim on it either*. If he really want's a Gondolin blade, he can simply take one of the ones in the Troll cache (the Dwarves said they were planning to come back and pick up the rest of it, and I see no reason why they wouldn't once things were settled). Burying a king or warrior with his weapons is the NORMAL thing to do in ME. Had Ganadalf fallen in the battle of the five armies, there is no doubt he would have been buried with Glamdring, had Bilbo, with Sting. There's no more extra honor in the decision to bury Orchrist with Thorin than with putting Boromir's weapons and cloven hunting horn in the boat with him. They're his, so they stay with him.
*Though I do not doubt that, had the fighting in the War of the Ring ever gotten bad enough to make such a desperate action necessary (and for some reason the troll cache had been lost or destroyed), Dain might have ordered, Thorin's tomb opened and Orchrist retrieved, if he thought that a Gondolin blade, with its proven history of being particularly effective against orc-kind would be a game changer in his battles (sort of like my theory that, had the Shadow returned in later years (as Tolkien one started to write), and King Eldarion had been aware of their existence,he might have sent men to the Barrow downs to exhume them in hopes of uncovering MORE shadow killing weapons of Cardolan, in hopes hey might provide an edge in the fight)
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