The touchstone site Catalogues of Enlightenment (Planar Handbook 166-7) grants this as its base ability: "Choose a cleric domain; you gain the granted power of that domain." Further, the Catalogues grants this as its higher order ability:

Once per day, you may cast a spell from the cleric domain you have chosen, as though you had prepared the spell normally. You must be of sufficient character level to cast the spell and have a Wisdom equal to 10 + the spell's level. (167)

(So you know, while that could be awesome (see below), a creature can employ this higher-order ability only 3 times—ever—before needing to go back to Mechanus's Fortress of Enlightenment and spend, usually, several weeks recharging the special ability.) Earlier the text says, "All higher-order abilities are considered either supernatural or spell-like, as indicated in each ability’s description" (154). Obviously, this higher order ability's description doesn't indicate it's a spell-like or supernatural ability, and, instead, the creature appears to be casting spells normally. But I don't know.

Questions

1. Is a creature's effective cleric level for the granted power of the picked domain its hit dice (as per a typical spell-like and supernatural ability: "If no caster level is specified, the caster level is equal to the creature’s Hit Dice" (MM 315)) or is the creature's cleric level its actual cleric level (which, in most cases, is nonexistent)? Or is there another option?

   For example, a creature with no cleric levels picks for its feat Planar Touchstone¹ the touchstone site Catalogues of Enlightenment and picks the domain Travel (PH 188-9). Does the domain's granted power—the freedom of movement-like effect against magical effects—occur automatically for a number of rounds per day equal to either the creature's Hit Dice or the creature's cleric level (hence no rounds)?

2. Is the higher order ability a spell-like or supernatural ability? Is the higher order ability, instead, the ability to actually cast spells? Or is the higher order ability merely granting access to different spells?

   If the higher order ability is spell-like or supernatural, this becomes much less of an issue. As mentioned above, a creature's Hit Dice then equals its caster level. But, when the higher order ability says that a creature must be of "sufficient character level to cast the spell," is that just code for the creature possessing, for example, at least 1 HD to cast a 1st-level spell, 3 HD to cast a 2nd-level spell, 5 HD to cast a 3rd-level spell, and so on, as if the creature were using its Hit Dice as its virtual cleric level? (That is, alternatively, for example, can a creature Dumpster-dive through standard and prestige classes that get access earlier to spells the picked domain grants and cast such spells earlier than likely expected if the creature possesses sufficient Wisdom?)

   But I don't know if the phrase as though you had prepared the spell normally is descriptive or prescriptive. If it's descriptive, that's fine, and these virtual spells can go back to being spell-like or supernatural abilities. But if it's prescriptive, a creature might, instead, need to have already the ability to cast spells (that is, its own casting class, caster level, and spell slots), and the Catalogues' spells can be cast only as substitutes for the creature's existing spells.

   For example, the creature above possesses 17 Hit Dice and Wisdom 19 yet no capacity to cast spells.² Can the creature cast 1/day three times per recharge employ the spell astral projecton?

Context: The creature in question is an advanced marut inevitable (usually 15 HD and Wis 17, this one 22 HD and Wis 19) that's an opponent for some (surprise!) high-level PCs. I wanted to give it a bit more oomph by providing the creature with some spells. I was considering the Spell Compendium domain Inquisition (275-6).

¹ Or, more likely, the feat Touchstone (Sandstorm 53) because it's easier to meet that feat's prerequisites (i.e. break a 250 gp object).
² Obviously, the creature is an NPC.