I'm playing Brielle who has an ability to bury a card to add a d12 to her charisma check. Is it permissible to use this ability for a Diplomacy check? It seems like it should but then could you apply the same principle for a strength/melee or dexterity/ranged with some allies (provided it doesn't specify non-combat, of course).
Yes, in Brielle's case a Diplomacy check is based on her Charisma skill, so any power that applies to Charisma also applies to Diplomacy.
The applicable rule can be found on page 11 of the Mummy's Mask Rulebook (since Brielle is pre-Core):
"The skill you're using for the check, and any skill referenced by that skill, are added as traits to the check. For example, if your character has the skill Melee: Strength +2, and you are using your Melee skill, both the Strength and Melee traits are added to the check..."
This was phrased more clearly in the Core Set Rulebook:
"The skill you chose from the list, the skill you're using, and any skill referenced by that skill, are all added as traits to the check. For example, if you choose combat from the list, then play a weapon that lets you use your Ranged skill for a combat check, and your range [sic] skill is "Dexterity +2," the check is a Dexterity Ranged combat check."