Learn German: Der neue Stundenplan hängt in der Schule. - The new timetable is hanging in the school.

The preposition in is a two-way preposition. Because the timetable is already hanging there (answering the question 'where?' or wo?) and not moving to a new location, we use the dative case. Schule is feminine, so its dative article is der.

Why does the adjective neue end in -e here?

It follows the rules for weak adjective declension. We already have the definite masculine article der, which clearly shows the nominative case and masculine gender. Because the article does this 'heavy lifting', the adjective just gets the basic -e ending.

Is the verb hängt here describing an action or a state?

Here it describes a state (where something is currently hanging). This means it uses the strong verb forms (hängen, hing, hat gehangen). If someone were actively putting the timetable on the wall, it would be a directed action using the weak verb forms (hängen, hängte, hat gehängt) and would take the accusative case (in die Schule).

Why is there an -n- in the middle of Stundenplan?