Learn Hardcore German: Im neuen Konferenzraum hängen große Diagramme an der Wand. - In the new conference room large diagrams are hanging on the wall.

Both are grammatically correct and mean the same thing. In spoken and written German, the contracted form im is strongly preferred unless you want to emphasize dem for some special reason (which is rare).

Why does neuen end in -en in im neuen Konferenzraum?

This is about adjective endings with the dative case and a definite article.

Konferenzraum is masculine: der Konferenzraum
After the preposition in (with a static location), you use dative: in dem Konferenzraum
With a definite article (dem), adjectives take the weak ending in dative singular masculine: -en

Pattern:

dative masculine: in dem neuen Konferenzraum → contracted: im neuen Konferenzraum

So neuen is dative masculine singular, weak declension after dem.

Why is the verb hängen in plural form?

The verb always agrees with the subject in number and person.

The subject here is große Diagramme:

Diagramme is plural (singular would be Diagramm)
Therefore the verb must be 3rd person plural: sie hängen → hängen

If it were singular, you would say:

Im neuen Konferenzraum hängt ein großes Diagramm an der Wand.

How do I know that große Diagramme is the subject and not an object?

A few clues:

Verb type
Here hängen is used intransitively (no direct object). It describes the state of the diagrams. That makes große Diagramme the thing whose state is described → the subject.
Typical pattern with location
In sentences like:
- An der Wand hängt ein Bild.
- Auf dem Tisch liegt ein Buch.
- Im Regal stehen viele Ordner.
  the object that is hanging/lying/standing is the subject.
Case marking
In plural, nominative and accusative have the same form (große Diagramme either way), so you can’t see the case from the ending here. You rely on grammar patterns and meaning: diagrams hanging makes sense as subject, but hanging the wall doesn’t.

Why is it große Diagramme and not großen Diagramme or großer Diagramme?

Große here is an adjective in front of a plural noun without any article.

Case: nominative plural (subject)
Article: none (no die, no viele, no meine, etc.)
Adjective declension: strong

Strong declension, nominative plural ending: -e

So:

nominative plural, no article: große Diagramme
If you had a definite article, it would be: die großen Diagramme (weak declension → -en)

Why is it an der Wand and not an die Wand?

This is the two-way preposition rule (Wechselpräposition):

With an, use dative for location (no movement)
Use accusative for movement toward something

Here, the diagrams are already hanging on the wall (a location, a state), so:

an der Wand → dative (static position)

If you describe movement towards the wall, you use accusative:

Wir hängen die Diagramme an die Wand.
(We hang the diagrams onto the wall.)

Why is it der Wand and not die Wand?

Wand is a feminine noun:

nominative: die Wand
accusative: die Wand
dative: der Wand
genitive: der Wand

The preposition an takes dative here because it describes a static location (the diagrams are hanging on the wall), so you must use:

an der Wand (feminine dative singular)

Why does in take the dative in im neuen Konferenzraum, and an take the dative in an der Wand?

Both in and an are two-way prepositions (Wechselpräpositionen).

They follow this pattern:

Dative → Where? (location, no movement)
Accusative → Where to? (movement/direction)

In this sentence:

im neuen Konferenzraum answers Where are the diagrams? → location → dative (dem Konferenzraum)
an der Wand answers Where are they hanging? → location → dative (der Wand)

If there were movement, you’d switch to accusative:

Wir gehen in den Konferenzraum. (into the room)
Wir hängen die Diagramme an die Wand. (onto the wall)

Why does the sentence start with Im neuen Konferenzraum and not with Große Diagramme?

German has a verb-second rule in main clauses: the finite verb (here hängen) must be in second position.
Position 1 can be almost anything: a subject, time phrase, place phrase, etc.

In your sentence:

Im neuen Konferenzraum (place phrase)
hängen (finite verb)
große Diagramme (subject)
an der Wand (additional location detail)

You could also say:

Große Diagramme hängen im neuen Konferenzraum an der Wand.

This version puts the subject first but still keeps the verb in second position. Both orders are correct; fronting Im neuen Konferenzraum just emphasizes the location.

Can I move an der Wand to a different place in the sentence?

Yes. German word order is quite flexible for these adverbial phrases (place phrases), as long as the verb stays in 2nd position. Possible variants include:

Im neuen Konferenzraum hängen an der Wand große Diagramme.
Im neuen Konferenzraum hängen große Diagramme an der Wand.
Große Diagramme hängen im neuen Konferenzraum an der Wand.
An der Wand hängen im neuen Konferenzraum große Diagramme.

The differences are mainly about emphasis and information structure, not grammar.

What is the difference between hängen and sein here? Could I say Im neuen Konferenzraum sind große Diagramme an der Wand?

You can say that, and it’s grammatical:

Im neuen Konferenzraum sind große Diagramme an der Wand.

Differences in nuance:

hängen focuses on how they are positioned → they are hanging
sein is more general, just saying that they are there

So:

Im neuen Konferenzraum hängen große Diagramme an der Wand.
→ highlights the fact that they are hanging (as opposed to standing, lying, etc.)
Im neuen Konferenzraum sind große Diagramme an der Wand.
→ just says they exist there; less specific about the manner of placement.

In most natural contexts when talking about pictures, diagrams, posters, etc., Germans prefer hängen.