Can you cast the Conjure Elemental spell to summon an elemental within the area of effect of the Forbiddance spell?

Question

The forbiddance spell description states:

You create a ward against magical travel that protects up to 40,000 square feet of floor space to a height of 30 feet above the floor. For the duration, creatures can't teleport into the area or use portals [...] to enter the area. The spell also proofs the area against planar travel, and therefore prevents creatures from accessing the area by way of the Astral Plane, Ethereal Plane, Feywild, Shadowfell, or the plane shift spell.

In addition, the spell damages types of creature that you choose when you cast it. Choose one or more of the following - celestials, elementals, fey, fiends, and undead. When a chosen creature enters the spell's area or starts its turn there, the creature takes 5d10 radiant or necrotic damage (your choice when you cast this spell). [...]

Can you cast the conjure elemental spell to summon an elemental within the area of effect of the forbiddance spell?

Answer 1

Yes, conjure elemental will work

Nowhere in the description of conjure elemental is it described as summoning the creature from another plane:

You call forth an elemental servant. Choose an area of air, earth, fire or water that fills a 10-foot cube within range. An elemental of challenge rating 5 or lower appropriate to the area you chose appears in an unoccupied space with 10 feet of it. For example, a fire elemental emerges from a bonfire, and an earth elemental rises up from the ground.

From the description of the spell we can see that you are calling the elemental out of the existing environment. Not summoning it from another plane. Therefore forbiddance does not prevent it.

However...

It will still take damage

If the caster of forbiddance selects the elemental creature type, your conjured creature will take the damage when it is summoned and again at the start of each of its turns so long as it is within the area of forbiddance. You should keep this in mind when choosing which creature types to ward the area against.

Answer 2

No, conjure elemental will NOT work.

From Monster Manual page 123:

"Conjured by Magic. Certain spells and magic items can conjure an elemental, summoning it from the Inner Planes to the Material Plane."

The Ethereal Plane is a border between the Material Plane and the Inner Planes.

The forbiddance spell description states:

"The spell also proofs the area against planar travel, and therefore prevents creatures from accessing the area by way of the Astral Plane, Ethereal Plane..."

Since you have no access to the Ethereal Plane therefor you have no access to the Inner Planes and you cannot conjure elemental.

It doesn't matter that the spell description doesn't specify it. It is specified in the description of "elementals", MM p.123, specifying what is an "elemental".