Die erste Besichtigung ist am Freitag, und wir wollen die Wohnung gemeinsam besichtigen.

Because Besichtigung is a feminine noun in German, so its basic article is die.

• die Besichtigung = the viewing / inspection
• erste is an adjective meaning first

Here, the noun phrase is in the nominative singular because it is the subject of the sentence: Die erste Besichtigung ist am Freitag.

After die in this pattern, the adjective takes -e:

• die erste Besichtigung

Besichtigung is a noun made from the verb besichtigen.

• besichtigen = to view, inspect, look at
• die Besichtigung = the viewing, the inspection

This is very common in German: a verb and a related noun often exist side by side.

In this sentence, you see both:

• Die erste Besichtigung = the first viewing
• die Wohnung besichtigen = to view the apartment

So German is using the noun once and the verb once.

Am is a contraction of an dem.

• an dem Freitag → am Freitag

With days of the week, German often uses an + dative, and this is usually contracted to am:

• am Montag = on Monday
• am Freitag = on Friday

So although English says on Friday, German normally says am Freitag.

There actually is, but German expresses it differently.

English:

• on Friday

German:

• am Freitag

So the idea of on is built into am here. You do not say just Freitag in this sentence, because ist Freitag would mean something more like it is Friday, not it is on Friday.

Because the second clause uses the modal verb wollen.

German modal verbs usually work like this:

• the conjugated modal verb comes in the normal verb position
• the main verb in the infinitive goes to the end

So:

• wir wollen die Wohnung gemeinsam besichtigen

Breakdown:

• wir = we
• wollen = want
• die Wohnung = the apartment
• gemeinsam = together
• besichtigen = view

This is a very important German sentence pattern:

• Ich will Deutsch lernen.
• Sie kann gut kochen.
• Wir wollen die Wohnung besichtigen.

Because after a modal verb like wollen, German normally uses the bare infinitive without zu.

So you say:

• Wir wollen die Wohnung besichtigen.

Not:

• Wir wollen die Wohnung zu besichtigen.

Other modal verbs work the same way:

• Ich kann schwimmen.
• Du musst gehen.
• Sie darf kommen.

Gemeinsam means together.

In this sentence:

• wir wollen die Wohnung gemeinsam besichtigen = we want to view the apartment together

It functions like an adverb, and it comes before the final infinitive besichtigen.

That placement is very natural in German. You may also hear slightly different word orders depending on emphasis, but this version is standard and clear.

Because Wohnung is a feminine noun:

• die Wohnung = the apartment

Here it is the direct object of besichtigen, so it is in the accusative. But for feminine nouns, the article is still die in both nominative and accusative singular.

So:

• nominative: die Wohnung
• accusative: die Wohnung

That is why the form does not change here.

Both are possible.

German allows different word orders depending on what you want to emphasize.

• Die erste Besichtigung ist am Freitag.
  Focuses more naturally on the first viewing
• Am Freitag ist die erste Besichtigung.
  Focuses more on Friday

In a main clause, the finite verb still has to stay in second position, so if Am Freitag comes first, ist must come next:

• Am Freitag ist die erste Besichtigung.

Because und connects two main clauses, and the second clause keeps normal main-clause word order.

So you get:

• Die erste Besichtigung ist am Freitag, und wir wollen die Wohnung gemeinsam besichtigen.

After und, German does not automatically send the verb to the end. That happens with many subordinating conjunctions such as weil, dass, or wenn, but not with und.

Compare:

• ..., und wir wollen die Wohnung besichtigen.
• ..., weil wir die Wohnung besichtigen wollen.

Because all nouns are capitalized in German.

In this sentence, the nouns are:

• Besichtigung
• Freitag
• Wohnung

This is one of the most noticeable differences from English. In German, capitalization is a useful clue that a word is a noun.