Die Schlüsselübergabe dauert nur wenige Minuten, wenn der Mietvertrag schon unterschrieben ist.

Because German very often makes compound nouns by joining smaller nouns into one word.

• der Schlüssel = key
• die Übergabe = handover, transfer

So die Schlüsselübergabe literally means key handover.

A useful rule: in German compounds, the last part is the main noun, and it decides the gender. Since Übergabe is feminine, Schlüsselübergabe is also feminine: die Schlüsselübergabe.

German nouns have grammatical gender, and you usually have to learn each noun with its article.

• die Übergabe → feminine
• der Vertrag → masculine

That is why:

• die Schlüsselübergabe
• der Mietvertrag

In compounds, the last noun controls the gender:

• Schlüsselübergabe ends in Übergabe → die
• Mietvertrag ends in Vertrag → der

It is another compound noun:

• die Miete = rent
• der Vertrag = contract

So der Mietvertrag means rental agreement / lease / tenancy contract, depending on context.

Again, the last part determines the gender, so it is der Mietvertrag because der Vertrag is masculine.

Because the subject is Die Schlüsselübergabe, which is a singular noun phrase.

Even though Schlüssel looks plural in form, the whole word Schlüsselübergabe is one singular noun meaning the key handover. So the verb agrees with that singular subject:

• Die Schlüsselübergabe dauert ...

If the subject were plural, the verb would change:

• Die Schlüsselübergaben dauern ...

This means only a few minutes.

• nur = only
• wenige = few
• Minuten = minutes

So dauert nur wenige Minuten means takes only a few minutes.

This is a very common way to talk about duration in German. You could also hear:

• dauert nur ein paar Minuten
• dauert nur einige Minuten

But nur wenige Minuten sounds very natural.

Here Minuten is in the accusative plural, used to express duration after dauern.

With no article before a plural noun, the adjective takes a strong ending. In the accusative plural, that ending is -e:

• wenige Minuten

So this is correct:

• Die Schlüsselübergabe dauert nur wenige Minuten.

You would see wenigen Minuten in other structures, for example after certain prepositions or in the dative:

• in wenigen Minuten = in a few minutes

Because wenn der Mietvertrag schon unterschrieben ist is a subordinate clause, and in German subordinate clauses are separated by a comma.

So the structure is:

• main clause: Die Schlüsselübergabe dauert nur wenige Minuten
• subordinate clause: wenn der Mietvertrag schon unterschrieben ist

German uses commas with subordinate clauses much more consistently than English does.

Here wenn means if or sometimes when for a condition or a repeated situation.

In this sentence it is basically if:

• ... wenn der Mietvertrag schon unterschrieben ist = ... if the rental contract is already signed

Important differences:

• wenn = if / whenever / when in general or repeated situations
• wann = when? used in direct and indirect questions
• als = when, but only for a single event in the past

Examples:

• Wenn er Zeit hat, kommt er. = If he has time, he comes.
• Wann kommt er? = When is he coming?
• Als ich klein war ... = When I was little ...

So wann would be wrong here.

Because wenn introduces a subordinate clause, and in German subordinate clauses the conjugated verb usually goes to the end.

That is why you get:

• wenn der Mietvertrag schon unterschrieben ist

not:

• wenn der Mietvertrag ist schon unterschrieben

This is one of the most important German word-order rules.

In a normal main clause, you would say:

• Der Mietvertrag ist schon unterschrieben.

But after wenn, the clause becomes subordinate, so the verb part moves to the end:

• ..., wenn der Mietvertrag schon unterschrieben ist.

So the difference is mainly word order.

• main clause: ist unterschrieben
• subordinate clause: unterschrieben ist

Yes, it is best understood as a state passive or resulting-state expression.

• Der Mietvertrag ist unterschrieben. = The contract is signed / has been signed.

This focuses on the state or result: the contract is in a signed state.

Compare:

• Der Mietvertrag wurde unterschrieben. = The contract was signed.
  This focuses more on the action/event.

In your sentence, the important idea is the condition being fulfilled already, so ist unterschrieben fits very well.

Here schon means already.

So:

• der Mietvertrag schon unterschrieben ist = the rental contract is already signed

It suggests that this step has been completed before the key handover happens.

In context, schon often gives the sense of by that point already.

Because in German, all nouns are capitalized.

So you get:

• die Schlüsselübergabe
• der Mietvertrag
• Minuten

This is a standard rule of German spelling and one of the easiest visual clues for spotting nouns in a sentence.

Yes. German allows that, and it is very common:

• Wenn der Mietvertrag schon unterschrieben ist, dauert die Schlüsselübergabe nur wenige Minuten.

Notice what happens in the main clause after the subordinate clause: the verb comes first in the main-clause part:

• ..., dauert die Schlüsselübergabe ...

This is because the whole wenn clause takes the first position, so the finite verb dauert must come immediately after it.

It can be understood as a general statement or a statement about a typical procedure.

German often uses the present tense for this kind of thing:

• Die Schlüsselübergabe dauert ... = The key handover takes ...
• ... wenn der Mietvertrag schon unterschrieben ist. = ... if the rental contract is already signed.

So even if the situation is in the future, German often still uses the present tense here, just like English often does in similar cases.