Das tropfende Rohr hinter dem Schrank nervt uns schon lange, aber der Abfluss ist jetzt das größere Problem.

Das tropfende Rohr uses a present participle as an adjective.

• tropfen = to drip
• tropfend = dripping
• das tropfende Rohr = the dripping pipe

So instead of making a full clause like das Rohr, das tropft, German can compress it into a noun phrase with an adjective-like form.

The ending -e on tropfende is there because it comes after das and describes Rohr.

Because in German, adjectives before nouns must take an adjective ending.

Here:

• das Rohr is neuter
• it is in the nominative
• it is preceded by the definite article das

So the adjective takes the weak ending -e:

• das tropfende Rohr

This is the same pattern as:

• das kalte Wasser
• der alte Schrank
• die kaputte Lampe

Because hinter is a two-way preposition. That means it can take either:

• dative for location
• accusative for direction/movement toward

Here the meaning is location: the pipe is behind the cupboard, not moving there.

So:

• hinter dem Schrank = behind the cupboard/in the position behind it

Compare:

• Das Rohr ist hinter dem Schrank. = The pipe is behind the cupboard.
• Ich stelle das Rohr hinter den Schrank. = I put the pipe behind the cupboard.

Because Schrank is a masculine noun: der Schrank.

After hinter with a location meaning, German uses the dative, and the masculine dative singular article is dem.

So:

• nominative: der Schrank
• dative: dem Schrank

nerven means to annoy, to get on someone's nerves, or to bother.

In this sentence:

• Das tropfende Rohr = the subject
• nervt = annoys
• uns = us

So Das tropfende Rohr nervt uns literally means:

• The dripping pipe annoys us

German uses the accusative object after nerven, so wir becomes uns.

Compare:

• Es nervt mich. = It annoys me.
• Es nervt dich. = It annoys you.
• Es nervt uns. = It annoys us.

Schon lange means for a long time already or simply for a long time.

In this sentence:

• nervt uns schon lange = has been bothering us for a long time

It suggests the annoyance is not new.

Similar examples:

• Ich warte schon lange. = I’ve been waiting for a long time.
• Das Problem besteht schon lange. = The problem has existed for a long time.

No, aber does not change the normal word order.

After aber, German starts a new main clause, and the conjugated verb still comes in second position:

• ..., aber der Abfluss ist jetzt das größere Problem.

So the structure is:

• der Abfluss = subject
• ist = verb
• jetzt = adverb
• das größere Problem = complement

This is different from words like deshalb or trotzdem, which count as sentence elements and can trigger inversion:

• Deshalb ist der Abfluss...

But aber is just a coordinating conjunction, like but in English.

Der Abfluss usually means drain.

Depending on context, it can refer to:

• the drain itself
• the drainage outlet
• sometimes the drainpipe/waste outlet area

In this sentence, it means that although the dripping pipe has been annoying, the drain is now the bigger issue.

It is a masculine noun:

• der Abfluss

Because Problem is a neuter noun in German:

• das Problem

So when it is described with an adjective after das, you get:

• das größere Problem = the bigger problem

The adjective größer is the comparative of groß:

• groß = big
• größer = bigger

And because it comes before the neuter noun with the definite article das, it takes the ending -e:

• das größere Problem

That is the normal comparative form of groß.

• groß = big
• größer = bigger
• am größten = biggest

The vowel changes from o to ö, which is common in some German comparatives.

Examples:

• ein großes Haus = a big house
• ein größeres Haus = a bigger house
• das größte Haus = the biggest house

German adverbs like jetzt are often placed in the middle field, after the verb and before later sentence elements.

Here:

• der Abfluss ist jetzt das größere Problem

This sounds natural and emphasizes that now, at this point, the drain is the bigger issue.

You could move elements around for emphasis, but the sentence as given is very standard.

Yes:

Das tropfende Rohr hinter dem Schrank nervt uns schon lange, aber der Abfluss ist jetzt das größere Problem.

First clause:

• Das tropfende Rohr hinter dem Schrank = subject noun phrase
  • das = the
  • tropfende = dripping
  • Rohr = pipe
  • hinter dem Schrank = behind the cupboard
• nervt = annoys
• uns = us
• schon lange = for a long time already

Second clause:

• aber = but
• der Abfluss = the drain
• ist = is
• jetzt = now
• das größere Problem = the bigger problem

So structurally it is:

• [Subject] [verb] [object] [time expression], but [subject] [verb] [adverb] [predicate noun phrase].

Yes. It is basically a shorter way of expressing something like:

• Das Rohr, das hinter dem Schrank ist und tropft, ...
• or more naturally:
• Das Rohr hinter dem Schrank, das tropft, ...

German often prefers this compact adjective style when possible:

• das tropfende Rohr instead of das Rohr, das tropft

This is very common and worth getting used to, because German uses such adjective constructions more often than English does.

Yes, there are three useful case points:

1. Das tropfende Rohr

   • nominative, because it is the subject of nervt

2. dem Schrank

   • dative, because hinter describes location here

3. uns

   • accusative, because it is the object of nervt

Then in the second clause:

• der Abfluss is nominative as the subject
• das größere Problem is also nominative in the sense of a predicate noun after sein

So this sentence is a nice example of how German marks roles through articles and pronouns.