Relic Reborn: Navel (Titan) Hard not showing up in duty finder

[Alberel]

My mistake, I did find the entrance to turn in 'in a titan spot'. The tunnels were just well hidden. Now I've got Navel (Hard) in my duty list, though it has a lock on it.

The lock probably means your iLvl is too low to do the trial yet. What is your average item level? You may need to upgrade some equipment.

Isn't the Titan Aetheryte outside of the mine, in the canyon between Iron Lake and Bronze Lake? Or was this Aetheryte only for the storymode Titan?

The aetheryte in the canyon is only for story mode titan. For HM and EX you need to reach the one in the mines.