How does the Commune spell work when cast by someone with the Ritual Caster feat or a warlock with the Book of Ancient Secrets invocation?

The D&D 5e spell Commune is a Cleric spell that contacts the Cleric’s chosen divine proxy and asks them three ‘yes or no’ questions. It is a ritual spell, so a Warlock with Book of Shadows or anyone with the Ritual Caster feat really can learn and cast the spell.

Let’s say an atheist wizard uses the Ritual Caster feat to learn Commune (gaining Ritual Caster does not require belief in any pantheon) and then casts it (which can be done through an arcane focus). Who would she encounter? (If it helps, the Wizard belongs to the School of Divination.)

If an Ancient Metallic Dragon uses Change Shape to turn into a humanoid with Innate Spellcasting, do the uses of “X/day” spells reset each time?

Ancient Metallic Dragons (e.g. Ancient Brass Dragons) have the Change Shape ability:

Change Shape. The dragon magically polymorphs into a humanoid or beast that has a challenge rating no higher than its own, or back into its true form. It reverts to its true form if it dies. Any equipment it is wearing or carrying is absorbed or borne by the new form (the dragon’s choice).

In a new form, the dragon retains its alignment, hit points, Hit Dice, ability to speak, proficiencies, Legendary Resistance, lair actions, and Intelligence, Wisdom, and Charisma scores, as well as this action. Its statistics and capabilities are otherwise replaced by those of the new form, except any class features or legendary actions of that form.

It is my understanding that the Spellcasting feature is a class feature and thus unavailable to an Ancient Metallic Dragon, but that the Innate Spellcasting trait is available to them.

Now, let’s take in example the Gloom Weaver humanoid from Mordenkainen’s Tome of Foes (p. 224), who has the following not-at-will Innate Spells:

1/day each: arcane gate, bane, compulsion, confusion, true seeing

If, say, an Ancient Brass Dragon decides to use Change Shape to turn into a Gloom Weaver, then decides to cast its 1/day true seeing, then uses Change Shape to revert to their dragon form, and uses it yet again to become a Gloom Weaver once more… does the dragon thus have a new use of true seeing?

In other words, does an ancient metallic dragon have essentially unlimited “X/day” innate spells by way of using Change Shape back and forth?

Does a spellcaster with Lair actions keep them when Shapechanging into an Ancient Metallic Dragon who then uses Change Shape?

A few high level arcane spellcasting monsters, such as the Lich from the Monster Manual, also have Lair Actions.

Such spellcasters can prepare then cast Shapechange on themselves to become an Ancient Metallic Dragon (such as a Brass one), while keeping some things :

You retain the benefit of any features from your class, race or other source and can use them, provided that your new form is physically capable of doing so.

It is my understanding that the above would allow the Lich to keep its Lair actions in dragon form.

Such dragons have a special Change Shape ability to transform into a humanoid or beast (such as a rabbit) while keeping certain things :

[…] retains its alignment, hit points, Hit Dice, ability to speak, proficiencies, Legendary resistances, lair actions, and Intelligence, Wisdom and Charisma scores, as well as this action.

It is clear from the Monster Manual’s Errata that the Lich could not gain the Dragon’s Lair actions (or the resulting beast/humanoid lair actions, if any) :

If a creature assumes the form of a legendary creature, such as through a spell, it doesn’t gain that form’s legendary actions, lair actions, or regional effects.

But what I’m wondering here is whether the now-twice-transformed creature would retain its initial form’s Lair actions. In this example, would the Lich-transformed-into-an-Ancient-Brass-Dragon-transformed-into-a-Rabbit keep its Lich Lair actions ?

Can a Tomelock swap the Book of Ancient Secrets invocation with itself upon level-up, and gain more than two ritual spells that way?

Eldritch Invocations (PHB, p. 107):

…Additionally, when you gain a level in this class, you can choose one of the invocations you know and replace it with another invocation that you could learn at that level.

Book of Ancient Secrets (BoAS) (PHB, p. 110):

Prerequisite: Pact of the Tome

You can now inscribe magical rituals in your Book of Shadows. Choose two 1st-level spells that have the ritual tag from any class’s spell list (the two needn’t be from the same list). The spells appear in the book and don’t count against the number of spells you know. With your Book of Shadows in hand, you can cast the chosen spells as rituals. You can’t cast the spells except as rituals, unless you’ve learned them by some other means. You can also cast a warlock spell you know as a ritual if it has the ritual tag.

On your adventures, you can add other ritual spells to your Book of Shadows. When you find such a spell, you can add it to the book if the spell’s level is equal to or less than half your warlock level (rounded up) and if you can spare the time to transcribe the spell. For each level of the spell, the transcription process takes 2 hours and costs 50 gp for the rare inks needed to inscribe it.

Assuming that the DM rules that the Rituals learned by BoAS don’t vanish upon dismissing (old) BoAS:

Is it possible by RAW to gain two new ritual spells with every warlock level by switching the BoAS invocation with the BoAS invocation upon level-up?

Bonus:

Assuming that the DM rules that the spells learned from BoAS vanish:

Can a warlock copy a spell from his Book of Shadows to his Book of Shadows and preserve the Spells in this way to get more ritual spells by switching BoAS with BoAS on level-up?

If a warlock with the Book of Ancient Secrets invocation swaps it out and takes the Ritual Caster feat, can they cast already-copied rituals?

I have a player that is playing a warlock. He wants to go Pact of the Tome and take the Book of Ancient Secrets eldritch invocation at level 3, but then replace it at a later with a different invocation. He keeps the book and at a later level takes the Ritual Caster feat.

Would the Ritual Caster feat permit him the ability to ritually cast the already transcribed rituals even if they are not of the chosen class from the feat?

Can another caster teach ritual spells to a Warlock with Book of Ancient Secrets? [duplicate]

This question already has an answer here:

  • Can Wizards, Tome Warlocks, and those with the Ritual Caster feat use spells from each other's books? 2 answers
  • What exactly are the sources from which you can copy spells into a Book of Shadows? 4 answers

Wizards, for example, are explicitly stated to copy spells from scrolls, and can only learn spells from scrolls. However, the Eldritch Invocation Book of Ancient Secrets is very general about how ritual spells can be learned:

On your adventures, you can add other ritual spells to your Book of Shadows. When you find such a spell, you can add it to the book if the spell’s level is equal to or less than half your warlock level (rounded up) and if you can spare the time to transcribe the spell.

“Finding such a spell on your adventures” seems very general. Specifically, could learning spells from another caster qualify?

My research topic: Golden ratio in ancient art

Φ is the golden ratio, 1,618… a is a positive number (not necessarily an integer). n is an integer (-∞, ∞).

Imagine two sets of numbers: aΦ^n and bΦ^n

If a/b (or b/a) is not a power of Φ, these two sets have no common element. In other words; if these two sets have one element in common, then they are the exact same set, and a/b (or b/a) is a power of Φ.

Is this statement true?

Thank you. Ates Gulcugil