The spell's Range/Area indicates it affects a 30 ft sphere, but the description says "within 30 feet of you". Does that mean the radius of the sphere is 30 ft or 15 ft?

Can this detect Quori?

I would say yes.

The creature types are:

Aberration, Beast, Celestial, Construct, Dragon, Elemental, Fey, Fiend, Giant, Humanoid, Monstrosity, Ooze, Plant, Undead.

Bolded are the types that this spell detects. Quori are definitely NOT any of the other types (Beast, Construct, Dragon, Giant, Humanoid, Monstrosity, Ooze, Plant).

They are probably Aberrations, Fey, or Fiends, but we don't have any stats on them.

‘Faithful of Eberron’ went with Aaberration as well. It’s not official, but it’ll do.

Basic rules say the following (regarding sphere shaped spells): "You select a sphere's point of origin,  and the sphere extends from that point. The sphere's size is expressed as a radius in feet that extends from the point."

Clearly, that means that the sphere's radius is 30 feet (diameter being 60 feet), meaning that you can Detect Evil and Good both 30 feet to your left and 30 feet to your right (and front and back and up and down) at the same time.

Hope this helps ;)

Allow me to set a scene for you...

BACKSTORY: You're the DM, I'm a player at your table. You have a evil cleric of some description that's presenting himself as a lawful good. As a player I don't trust this NPC. As a character I have been rolling nothing but 1's and 2's on 3 separate insight checks so my character thinks your cleric says some suspicious stuff sometimes, but otherwise he's legit. At this point I as a player feel like I have no control over the situation anymore. BUT! Another player doesn't bother rolling insight as they don't trust religious people as a rule of thumb (great role play with this other player at any other opportunity). This other player tells me to check him out to see how evil he really is (this cleric had mentioned ritual sacrifice, then clarified to my character that we all must make sacrifices like giving up things we cherish in order to become closer to our God's).

THE QUESTION: So I go to cast detect evil and good. This spell does not mention anything about alignment except the evil and good part in the title of the spell. Would I know that I'm dealing with an evil cleric at this point and safely assume that he's been lying/misleading me this entire time? 

I would say no, the spell is not meant to identify intangible evil/good alignments. Based on the spell description, it is used to identify the presence and location of physical things (e.g. the listed types of creatures, magic objects and locations.)

Would this spell detect possessions?

Quote from PearlsBefore4Swine >>

Would this spell detect possessions?

 Yes!

Does this spell detect things in the ethereal plane?  I ruled that the cleric couldn't detect a succubus while it was in the ethereal plane.

As far as I know, character alignment in 5e is never called upon by anything in the game. Consider it a player aid for role play and nothing more.

Quote from EeryPetrol >>

As far as I know, character alignment in 5e is never called upon by anything in the game. Consider it a player aid for role play and nothing more.

 This is not strictly true. For example, the Book of Exalted Deeds from the DMG

.

Quote from mikecheb >>

Quote from EeryPetrol >>

As far as I know, character alignment in 5e is never called upon by anything in the game. Consider it a player aid for role play and nothing more.

 This is not strictly true. For example, the Book of Exalted Deeds from the DMG

deals 24d6 radiant damage to any evil creature who tries to read it

 

.

 Also the Talisman of Ultimate Evil.

And, a sprite’s heart sense.

Look at the damage type for Spirit Guardians as well. 

Would this detect Aasimars and Tieflings?

Aasimar and Tieflings are humanoids, so it would not detect them.

Quote from ebrowne72 >>

Aasimar and Tieflings are humanoids, so it would not detect them.

 Just for clarification, if the tiefling was wielding a demon-possessed magical item, would this spell detect the presence of a demon? If the tiefling disobeyed the weapon and the demon possessed them, would the tiefling then trigger the spell's effects?

This spell only detects aberrations, celestials, elementals, fey, fiends, and undead within 30 feet of you.  That is all it does.  It doesn't tell you if those things are good or evil.  It doesn't tell you if items are good or evil, nor does it locate items for you.  It informs you if one or more the aforementioned types of creatures are close to you, and pinpoints their location.  That is all that it does.

Quote from Tor888 >>

Quote from ebrowne72 >>

Aasimar and Tieflings are humanoids, so it would not detect them.

 Just for clarification, if the tiefling was wielding a demon-possessed magical item, would this spell detect the presence of a demon? If the tiefling disobeyed the weapon and the demon possessed them, would the tiefling then trigger the spell's effects?

Is that demon-possessed magical item one of the types of creatures (most likely fiend) in and of itself?  Probably not, so no.  If the tiefling was then possessed by it, would its creature type change from humanoid to fiend?  Probably not, so no.  If your DM rules otherwise, then yes.

this spell needs to be renamed. and it's also nerfed to hell if it's supposed to have anything to do with the original spell.

Just read the spell.  The name doesn't define a spell.