Stonecunning itself is a fairly potent ability (considered proficient, add double proficiency bonus) that gets dramatically better when your proficiency bonus increases. Giving dwarves advantage on top of that won't be too problematic at low levels but at mid levels, that difference will probably be pretty noticeable. I personally don't have a problem with Dwarves being the undisputed experts on stonecraft but it's at least worth mentioning.
Beyond theme, though, advantage serves an important function. All dwarves normally get stonecunning, which means that dwarven clerics of Ulaa wouldn't gain any 1st level domain benefit, which seems out of line with other domains. This is also a throwback to the 3e Dwarf domain, which granted stonecunning to non-dwarves and doubled the bonus for dwarves.
Using Channel Divinity against air creatures: in 3e, the Earth domain power was to turn/rebuke air elementals. It's neat, but far more limited than the other 5e channel divinity powers. By opening up the turn effect to any creature with a fly speed the power is much more useful, and at much lower levels. It's power is still limited by the number of times per day that you can channel divinity: 1/rest from 1st-5th, 2/rest from 6th-17th, 3/rest from 18-20.
Advantage on Con checks: This ability is similar to the 6th level Dampen Elements ability for the Nature domain. It's not limited to a number of times per day because it's relatively situational. I also make it apply to all Con checks, not just Con saves. There are no Skills keyed to Constitution so I think it won't be overpowered. But by making the power affect skill checks you could potentially use it for the checks listed in the PHB: hold your breath, march or labor for hours without rest, go without sleep, survive without food or water, and especially, quaff an entire stein of ale in one go! lol!
Add acid or fire damage to weapon attacks: I added an additional energy type because a) fire (lava) and acid are both thematically correct and b) a few other domains grant multiple energy types and allow you to choose between them. I think the idea is to grant some flexibility to your combat ability without needing a specific magic weapon or spell, like in 3e.
Domain spells: I think they're pretty obvious choices. And I think StoneShape is the only cleric spell out of the group, which gives some nice flexibility to the Domain. I did swap out Elemental Weapon for Conjure Elemental because Elemental Weapon will be pretty redundant starting at 8th level and because Conjure Elemental isn't a clerical spell in 5e, which is weird. So let's give Earth clerics elemental buddies.
