Der Arzt, auf den wir im Wartezimmer gewartet haben, kam schließlich doch pünktlich.

Because the verb is warten auf = to wait for, and the preposition auf in this expression always takes the accusative.

So inside the relative clause, den refers back to der Arzt, but its form is determined by its role in the clause, not by the form of the noun in the main clause.

• main clause: Der Arzt = nominative, because he is the subject of kam
• relative clause: auf den = accusative, because warten auf requires it

That is why German says:

• der Arzt in the main clause
• auf den in the relative clause

Not auf dem, because that would be dative, and warten auf does not use dative.

In German, a relative pronoun changes form depending on its grammatical function inside the relative clause.

The noun it refers to is der Arzt, but inside the relative clause, that noun is not the subject. It is the object of the preposition auf in auf den wir ... gewartet haben.

So the relative pronoun has to match:

• gender/number of the noun: masculine singular, because it refers to der Arzt
• case required in the relative clause: accusative, because of warten auf

That gives den.

A useful way to think about it is:

• der Arzt tells you who we are talking about
• den tells you what role that person plays inside the relative clause

Because that part is a relative clause, and in German, relative clauses are separated by commas.

The structure is:

• Der Arzt = main clause element
• auf den wir im Wartezimmer gewartet haben = relative clause describing der Arzt
• kam schließlich doch pünktlich = rest of the main clause

So the commas show where the inserted descriptive clause begins and ends.

This is standard in German:

• Der Mann, den ich kenne, ...
• Das Buch, das auf dem Tisch liegt, ...

Because relative clauses are subordinate clauses, and in German subordinate clauses the finite verb goes to the end.

Here the tense is Perfekt, so the verbal parts are:

• gewartet = past participle
• haben = auxiliary verb

In a subordinate clause, both verbal parts go to the end, with the participle before the auxiliary:

• ..., auf den wir im Wartezimmer gewartet haben

Compare:

• main clause: Wir haben im Wartezimmer auf den Arzt gewartet.
• relative clause: ..., auf den wir im Wartezimmer gewartet haben

That verb-final word order is one of the most important features of German subordinate clauses.

Because in a subordinate clause using the Perfekt, the normal order is:

• other elements
• past participle
• auxiliary at the very end

So German prefers:

• ..., weil wir lange gewartet haben
• ..., auf den wir gewartet haben

not:

• ..., weil wir haben lange gewartet
• ..., auf den wir haben gewartet

In main clauses, the auxiliary is in second position:

• Wir haben gewartet.

In subordinate clauses, the auxiliary moves to the end:

• ..., weil wir gewartet haben.

Because the relative clause is inserted inside the main clause, but the main clause still follows the normal verb-second rule.

The first main-clause element is actually the whole noun phrase:

Der Arzt, auf den wir im Wartezimmer gewartet haben,

That entire chunk counts as the first element. After that, the finite verb of the main clause must come:

• kam

So the structure is:

1. Der Arzt, auf den wir im Wartezimmer gewartet haben,
2. kam
3. schließlich doch pünktlich

Even though the subject is long, it still occupies the first position as a single unit.

German relative clauses often use a relative pronoun with a preposition when the verb requires one.

English can say:

• the doctor who we waited for

German cannot leave the preposition hanging at the end like English often does. The preposition must stay with the pronoun:

• der Arzt, auf den wir gewartet haben

So German is closer to formal English:

• the doctor for whom we waited

But in normal German, this structure is completely standard, not especially formal.

im is a contraction of in dem.

So:

• im Wartezimmer = in the waiting room

Here it is a location phrase, answering where?, so in takes the dative:

• in dem Wartezimmer
• contracted: im Wartezimmer

This is different from warten auf, where auf is part of the verb and takes accusative for a completely different reason.

So in the same clause you have:

• im Wartezimmer = location, dative
• auf den = object of warten auf, accusative

Both are possible, but they mean slightly different things.

• Er war pünktlich = he was on time
• Er kam pünktlich = he arrived on time

In this sentence, kam pünktlich focuses on the moment of arrival. That fits well because people were waiting for the doctor, and then he arrived.

So pünktlich is describing how he came/arrived:

• kam pünktlich = arrived punctually / on time

These two words add nuance.

• schließlich often means in the end, after all, or eventually
• doch here suggests contrary to expectation or despite what seemed likely

So together, schließlich doch pünktlich means something like:

• was, in the end, actually on time after all
• did turn out to be on time after all

The speaker is suggesting that maybe it seemed as if the doctor might be late, but despite that, he ended up arriving on time.

So the combination adds a subtle feeling of:

• expectation of lateness
• final outcome: he was on time anyway

Yes, absolutely. German often mixes Perfekt and Präteritum, especially with common verbs like kommen, sein, haben, and modal verbs.

Here:

• gewartet haben describes the earlier action of waiting
• kam describes the later event of arriving

This combination is natural. In many styles of German, especially spoken language, Perfekt is common for many past actions, while Präteritum is still very common for certain verbs such as kam from kommen.

So the mixture is not strange. It can sound very normal.

Yes, you could say:

Der Arzt, auf welchen wir im Wartezimmer gewartet haben, ...

But this sounds more formal, heavier, and less natural in everyday German.

In ordinary German, the usual relative pronoun is:

• der, die, das
• and in this sentence: den

So auf den is the normal, idiomatic choice.

No. warten auf is not a separable-prefix verb. It is a normal verb plus a prepositional complement.

That means:

• infinitive: auf jemanden warten
• main clause: Wir warten auf den Arzt
• perfect: Wir haben auf den Arzt gewartet
• relative clause: ..., auf den wir gewartet haben

This is different from a true separable verb such as anrufen:

• Ich rufe ihn an
• Ich habe ihn angerufen

With warten auf, the auf belongs to the required preposition, not to a separable verb prefix.

Yes. The core idea could be split into two sentences:

• Wir haben im Wartezimmer auf den Arzt gewartet.
• Der Arzt kam schließlich doch pünktlich.

The relative clause version combines them by turning the first sentence into a description of der Arzt:

• Der Arzt, auf den wir im Wartezimmer gewartet haben, kam schließlich doch pünktlich.

This is a very common way German packs information into one sentence.