Bei der zweiten Besichtigung wollen wir auch den Keller besichtigen.

This is a time/context phrase meaning something like at the second viewing or during the second viewing.

• bei often means at, with, or during, depending on context.
• Here, bei der zweiten Besichtigung tells us when / on what occasion something will happen.

So the sentence is structured like:

• Bei der zweiten Besichtigung = at the second viewing
• wollen wir auch den Keller besichtigen = we also want to look at the basement

German often puts this kind of phrase at the beginning for emphasis or to set the scene.

Because bei takes the dative case.

The noun Besichtigung is feminine, so:

• nominative: die Besichtigung
• dative: der Besichtigung

And because there is a definite article (der), the adjective zweite changes to zweiten:

• die zweite Besichtigung = the second viewing
• bei der zweiten Besichtigung = at the second viewing

So both the article and the adjective are showing the dative feminine form.

Because it comes after a definite article and the whole phrase is in the dative feminine.

The pattern is:

• die zweite Besichtigung → nominative feminine
• bei der zweiten Besichtigung → dative feminine

After der in this kind of phrase, the adjective usually takes -en.

So:

• zweite = base form you often see in nominative feminine
• zweiten = the correct declined form here

This is a normal adjective ending pattern in German.

Because German main clauses follow the V2 rule: the finite verb must be in the second position.

Here, the sentence begins with Bei der zweiten Besichtigung, which counts as the first element. That means the finite verb must come next:

• Bei der zweiten Besichtigung | wollen | wir ...

So the order is:

1. fronted time/context phrase
2. finite verb: wollen
3. subject: wir

If you started with the subject instead, you could also say:

• Wir wollen bei der zweiten Besichtigung auch den Keller besichtigen.

That is also correct, just with a different emphasis.

The two words are related, but they are doing different jobs.

• Besichtigung is a noun: viewing, inspection
• besichtigen is a verb: to inspect, to view, to look at

So the sentence literally has something like:

• At the second viewing, we also want to view the basement.

This repetition may sound a bit clunky in English, but it is perfectly normal in German. German often uses related nouns and verbs in the same sentence without it sounding strange.

Because the sentence uses a modal verb: wollen.

In German, with a modal verb:

• the modal verb is the finite verb and goes in the normal main-clause position
• the main verb stays in the infinitive at the end

So:

• wollen = want to
• besichtigen = inspect / look at

Pattern:

• Wir wollen den Keller besichtigen.
  = We want to inspect the basement.

This is one of the most important German sentence patterns to learn.

Because Keller is the direct object of besichtigen, and direct objects take the accusative case.

The noun Keller is masculine:

• nominative: der Keller
• accusative: den Keller

So:

• der Keller = the basement (as subject)
• den Keller = the basement (as object)

In this sentence, we are doing the action, and the basement is what is being viewed, so German uses the accusative: den Keller.

Here auch means also / too, and it most naturally applies to den Keller besichtigen.

So the idea is:

• during the second viewing, we want to inspect the basement as well

This suggests that there are other things the speakers plan to look at too.

Its position is quite natural in German:

• wollen wir auch den Keller besichtigen

That does not usually mean we too want in the strongest sense. It more naturally means we also want to inspect the basement.

Yes. German word order is flexible, as long as the finite verb stays in second position in a main clause.

For example:

• Bei der zweiten Besichtigung wollen wir auch den Keller besichtigen.
• Wir wollen bei der zweiten Besichtigung auch den Keller besichtigen.

Both are correct.

The version with Bei der zweiten Besichtigung first puts more focus on when this will happen.

In this context, Besichtigung usually means a property viewing or house/apartment viewing.

It can also mean a more general inspection or tour, depending on context, but in a sentence with Keller and zweite Besichtigung, many learners will recognize it as the kind of viewing you do when looking at a house or apartment.

So die zweite Besichtigung is likely:

• the second viewing of the property

It can mean both, depending on context.

• Keller can be a basement
• it can also be a cellar

In property-related contexts, basement is often the most natural translation. In other contexts, especially where storage or wine is involved, cellar may fit better.

So the exact English word depends on the situation, but the German word is the same.