FEEL COMMAND:
"Exhaust this card when the overlord chooses a hexed monster to activate. Discards 1 hex token from that monster to immediately perform an attack with it. You make all choices during the attack. After the attack is resolved, the monster activates as normal."

Hexed Ariad is about to be activated by OL. Hexer uses Feel Command.

When attacking with Ariad can Hexer uses the abilities of elemental stones (like Burning Might (Red stone) - each attack gains 1 SURGE to the result) ??

Thank you for your answers.

Because the quest book describes the bonuses that Ariad gets from the elemental stones as "abilities" then I would say yes. Monster abilities are not like hero skills. The stones are essentially adding additional text fields to Ariad's monster card, and those are traditionally available to all who control that monster.

If the Hexer uses "Fel Command" on Ariad, they will have access to all of these bonuses.

On an unrelated note, "Feel Command" sounds like something a succubus or incubus would use