If an Elf Wizard regains all expended spell slots after a 4 hour rest (trance), then what good is Arcane Recovery?

Does an Elf Wizard regain all expended spell slots after a 4 hour rest (trance)?

It would appear that the answer here is yes, however, if that is the case, then what good is Arcane Recovery? (I understand these are separate questions but the answer to one will affect the other)

How does Arcane Armament interact with the Artillerist Artificer’s Wand Prototype feature?

The revised Artificer in Unearthed Arcana gets extra attack from its Arcane Armament feature (pg 5):

Arcane Armament: Starting at 5th level, you can attack twice, rather than once, whenever you take the Attack action on your turn, but one of the attacks must be made with a magic weapon, the magic of which you use to propel the attack.

The Artillerist sub class allows the Artificer to apply a cantrip to a wand through Wand Prototype (pg 8):

Wand Prototype: By 6th level, you now regularly experiment with channeling different types of magic through wands. Whenever you finish a long rest and your woodcarver’s tools are with you, you can touch a nonmagical, wooden wand and turn it into a magic item. When you do so, you invest it with one artificer cantrip of your choice—even one you don’t know—that has a casting time of 1 action. As an action, you can cause the magic wand to produce the cantrip, using your spellcasting ability modifier (other creatures are unable to use the wand’s magic). The wand loses this magic when you finish your next long rest.

Any damage roll you make for a cantrip in the wand gains a bonus equal to your Intelligence modifier (minimum of +1).

When you reach 14th level in this class, you can invest the wand with two cantrips at the end of a long rest.

How does Arcane Armament interact with the Artillerist Artificer’s Wand Prototype feat? Can you attack twice with the wand cantrip?

Do Arcane Ward’s starting hit points include the INT modifier once or twice?

An abjuration wizard’s Arcane Ward states:

[…] The ward has hit points equal to twice your wizard level + your Intelligence modifier.

So how many hit points is this supposed to be?

$ (2 \times WizardLevel) + INT_{mod}$

or

$ 2 \times (WizardLevel + INT_{mod})$ ?

I feel like the phrasing hints toward the first calculation, but it’s still somewhat ambiguous.

What is the number of Temporary HP you get from Wizard’s Arcane Ward?

I’m playing D&D 5e as a DM for about a 3-4 sessions now and the math involved in the Wizard’s ability Arcane Ward is a little unclear to me. All of my players just reached level 2 and one of the players is a Wizard who chose The School of Abjuration archetype and he now has the Arcane Ward ability.

Playing by the PHB(p.109) the ability states:

Starting at 2nd level, you can weave magic around yourself for protection. When you cast an abjuration spell of 1st level or higher, you can simultaneously use a strand of the spell’s magic to create a magical ward on yourself that lasts until you finish a long rest. The ward has hit points equal to twice your wizard level + your Intelligence modifier.


With his Intelligence modifier (+3) and Wizard level 2 the equation should be:

Temporary HP = ( 2 * Wizard level ) + Int modifier

Temporary HP = ( 2 * 2 ) + 3

Temporary HP = 4 + 3

Temporary HP = 7


But it can also be:

Temporary HP = 2 * ( Wizard level + Int modifier )

Temporary HP = 2 * ( 2 + 3 )

Temporary HP = 2 * 5

Temporary HP = 10


The text makes it unclear.

Does Arcane Eye transmit information if the caster moves to a different plane?

The description of arcane eye states that the eye created by the spell “can’t enter another plane of existence.” PHB p. 214.

Consider this scenario: a warlock casts arcane eye (perhaps using the Visions of Distant Realms invocation), creating an eye 30 feet away; subsequently casts demiplane; and then steps through the shadowy door created by demiplane, leaving behind the eye exactly where it was created.

What result? Is there any rules-as-written reason to rule otherwise than that the eye did not “enter” another plane, and so remains in existence and continues to transmit information across the planes? Or does the eye remain in existence but cease to transmit information? Or does it cease to exist? Or something else?

Can an Abjuration Wizard’s Arcane Ward only absorb damage from one attack using Projected Ward?

The School of Abjuration wizard’s Projected Ward feature (PHB, p. 115) says:

Starting at 6th level, when a creature that you can see within 30 feet of you takes damage, you can use your reaction to cause your Arcane Ward to absorb that damage. If this damage reduces the ward to 0 hit points, the warded creature takes any remaining damage.

Does this mean that you can only absorb damage from one attack using this feature?