The dragon stone isn't related to the crystals and dragon statues by Maxos temple, or to the 4 scrolls you can get ZixZax to translate (which gives you the password for a couple of teleporters).
You will get the dragon stone after you have completed the battle tower. It will be in your inventory after that, and can not be sold or dropped. If you have not defeated Laiken, keep going on Sentinel Island. You will want to finish off everything that you can in Broken Valley and Sentinel Island before confronting Laiken, as afterwards most open quests will fail (there is one in each region you can do later) and most NPCs and locations will be unavailable.
If you have gotten the battle tower and done the first dragon fight, you can use the dragon morph stone from your inventory or assign it to a hot key/button.
The sigil required for the Hall of Echoes quest can be found in Broken Valley after you have the battle tower. Given the level of opponents that will be there then, it would be better to complete some the fjords before returning there. There is no rush on the Hall of Echoes quests, since that is the final area of the game.
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