The Eluvians can go to different places; they can go to the halfway place that connects them to each other, or they can go to the Fade (but this requires power equivalent to what Flemeth has). Perhaps there are also other places they can go?
All Eluvians lead to the same place: The Crossroads. The only way you can go to a different place using an Eluvian is if you are in the Crossroads and take an Eluvian from there. If you enter an Eluvian in any place that is not the Crossroads, you will end up at the Crossroads.
Elven deities existed. Possibly as extremely powerful mages who 'ascended', possibly as actual gods and goddesses.
Solas himself says that he does not consider the Elven gods "gods" unless you stretch the meaning of the word to absurd levels. They certainly do not seem to possess qualities such as omniscience and omnipresence.
Something I saw earlier mentioned the codex entry about object permanence in the Fade, saying that only artificial things make sense in the Fade.
No, not "artificial things", only things man has shaped. Only things man has shaped act accordingly in the fade. The one who wrote the codex entry speculates that this is why rocks float - man has never shaped rocks, dwarves did, and the person who wrote the codex entry speculates that if dwarves could dream the rocks would behave "normally" in the fade.
We also know that the Golden City was golden, according to Corypheus.
No we don't, Corypheus directly states several times in both Legacy and DA:I that the City was not golden when they arrived. He says he only found desolation and corruption. Unless you are thinking of the line "I walked the Golden Halls", ask yourself; how cool would "I walked the Blackened Halls" sound? It's just there for dramatic effect.
But we do know that it's possible to reverse the Rite of Tranquility, by having a spirit/demon touch the mind of said Tranquil. Perhaps it's possible, in extremely unusual situations, for the same thing to happen to a dwarf?
Whoever gets healed from tranquility, as stated by Cassandra, has a very high chance of being emotionally unstable. It doesn't leave them simpletons. Sandal, is for all intents and purposes, a savant, he is retarded but exceptionally good at one area.
But by now your conjecture begs these questions:
1) Why would June come to Sandal?
2) Why would it leave him retarded, since Flemeth seems fine?
3) What was the point of your earlier reasoning, since it does not directly support the theory?
4) If Sandal was retarded before June came to him, for what practical reason would June merge with him?
"Sandal is a savant in enchanting and crafting, thus he must be possessed by the Elven god of crafting" is quite a logical leap.