How do Aeon stones work?

I thought once you use the Aeon stone's active effect (like the spell that some might have) it becomes consumed, but I cant find anywhere that says that, neither in the 1e rules nor in the 2e rules.

Anyone know the answer?

The only Aeon Stone currently that gets consumed is the Delaying one. Its invested ability is that if you would die from your Dying value increasing, It instead sets your dying value to one less of what would kill you.

Otherwise these are permanent items, Their usual effect takes hold whenever you invest in it, causing it to orbit around your head.

Their resonant power is gained from placing them in a wayfinder, of which you usually only can have one actively granting you its benefit.

So, for Dusty Rose Prism, we have "This aeon stone allows you to cast the 1st-level shield cantrip as an arcane innate spell, surrounding yourself in pink energy."

--> can this be done at will, 1/day, 1/hour, etc. 'As an arcane innate spell' means what?

2e says "Innate cantrips are cast at will and automatically heightened as normal for cantrip unless otherwise specified," which suggests you can use the shield cantrip at will (although in this case, the Dusty Rose Prism wording specifies it's the 1st-level version, and so you can't heighten it).

Just want to confirm this basically can be done each round on your turn if you want to...

So, for Dusty Rose Prism, we have "This aeon stone allows you to cast the 1st-level shield cantrip as an arcane innate spell, surrounding yourself in pink energy."

--> can this be done at will, 1/day, 1/hour, etc. 'As an arcane innate spell' means what?

2e says "Innate cantrips are cast at will and automatically heightened as normal for cantrip unless otherwise specified," which suggests you can use the shield cantrip at will (although in this case, the Dusty Rose Prism wording specifies it's the 1st-level version, and so you can't heighten it).

Just want to confirm this basically can be done each round on your turn if you want to...

until it's used to Shield Block. The stone's text doesn't say it overrides that limit

So, for Dusty Rose Prism, we have "This aeon stone allows you to cast the 1st-level shield cantrip as an arcane innate spell, surrounding yourself in pink energy."

--> can this be done at will, 1/day, 1/hour, etc. 'As an arcane innate spell' means what?

2e says "Innate cantrips are cast at will and automatically heightened as normal for cantrip unless otherwise specified," which suggests you can use the shield cantrip at will (although in this case, the Dusty Rose Prism wording specifies it's the 1st-level version, and so you can't heighten it).

Just want to confirm this basically can be done each round on your turn if you want to...

Yep! There's no usage limit or cooldown on it (or on the Shield spell if you just cast it), so you can use it as many times as you want. As Baarogue mentioned: the normal rules of the Shield spell apply, so once you use the reaction it gives, you can't cast it again for 10 minutes.

To clarify for other Aeon Stones, the reason that Dusty Rose Prism is at-will is because the spell is a Cantrip.

Polished Pebble has a resonant power that allows you to cast Grease. Grease is not a Cantrip, so it is not cast at-will. The rule text for the ability specifies that the spell is cast as an innate spell with a limit of 1 per day.