Wir würden lieber in einem Neubau wohnen, obwohl der Altbau von außen schöner aussieht.

würden wohnen is a Konjunktiv II construction, often used to express something hypothetical, tentative, or a preference like would live.

So:

• Wir wohnen ... = We live ...
• Wir würden ... wohnen ... = We would live ...

In this sentence, it helps express a preference rather than a simple fact:

• Wir würden lieber ... wohnen = We would rather live ...

German often uses würden + infinitive this way, especially in everyday speech.

Lieber means rather or preferably.

It comes from gern:

• gern = gladly / like to
• lieber = rather / prefer
• am liebsten = most preferably

So:

• Wir wohnen lieber in einem Neubau = We prefer to live in a new building
• Wir würden lieber in einem Neubau wohnen = We would rather live in a new building

Its position is normal: it appears before the part being preferred, here in einem Neubau wohnen.

Because in can take either the dative or the accusative, depending on meaning:

• dative for location: where?
• accusative for direction/movement toward: where to?

Here the sentence is about living in a place, so it describes location, not movement.

• in einem Neubau wohnen = to live in a new building

So the dative is required.

Since Neubau is masculine (der Neubau), the dative singular form is:

• einem Neubau

Compare:

• Wir wohnen in einem Neubau. = We live in a new building.
• Wir ziehen in einen Neubau. = We are moving into a new building.

These are very common German housing terms.

• der Neubau = a new building, usually a more modern one
• der Altbau = an older building, often one built before World War II

In German-speaking countries, Altbau often suggests a certain style: high ceilings, older architecture, decorative details, and often more charm.
Neubau often suggests better insulation, newer plumbing, elevators, modern layout, and fewer maintenance issues.

So this sentence reflects a very typical contrast in German real-estate language.

Because obwohl introduces a subordinate clause, and in German subordinate clauses are normally separated by a comma.

• main clause: Wir würden lieber in einem Neubau wohnen
• subordinate clause: obwohl der Altbau von außen schöner aussieht

So the comma is required.

Because obwohl is a subordinating conjunction, and in German subordinate clauses the conjugated verb goes to the end.

Main clause word order:

• Der Altbau sieht von außen schöner aus.

Subordinate clause after obwohl:

• ..., obwohl der Altbau von außen schöner aussieht.

So this is a standard word-order change caused by obwohl.

Yes, aussehen is a separable verb:

• infinitive: aussehen
• main clause: Er sieht gut aus.
• subordinate clause: ..., weil er gut aussieht.

In a main clause, the prefix separates:

• sieht ... aus

In a subordinate clause, the verb goes to the end and the prefix stays attached:

• aussieht

That is exactly what happens here.

Because der Altbau is the subject of the subordinate clause, so it must be in the nominative case.

Who looks nicer from the outside?

• der Altbau

That makes it the subject.

So:

• der Altbau = nominative
• den Altbau = accusative

Here the building is doing the looking/appearing, so nominative is correct.

Von außen means from the outside or externally.

So:

• Der Altbau sieht von außen schöner aus = The old building looks nicer from the outside

This phrase contrasts outward appearance with other qualities. The sentence suggests:

• the Altbau looks prettier from the outside,
• but they would still prefer living in a Neubau.

You may also see:

• von innen = from the inside
• von außen betrachtet = seen from the outside

Because schöner is not directly describing a noun here. It is a predicate adjective after aussehen.

Compare:

• ein schöner Altbau = a beautiful old building
  
  • adjective before a noun, so it takes an ending
• Der Altbau sieht schöner aus. = The old building looks more beautiful.
  
  • predicate adjective, so no ending

So in this sentence:

• schöner = more beautiful / prettier
• no adjective ending is needed

Because wohnen specifically means to live/reside somewhere, especially in the sense of housing or accommodation.

• wohnen = live somewhere, reside
• leben = live, be alive, lead one’s life more generally

Since the sentence is about preferring one type of building to live in, wohnen is the natural choice.

Compare:

• Wir wohnen in Berlin. = We live in Berlin.
• Wir leben gut. = We live well.
• Er lebt noch. = He is still alive.

In standard written German, yes: obwohl normally introduces a subordinate clause with the verb at the end.

So the standard form is:

• ..., obwohl der Altbau von außen schöner aussieht.

In casual spoken German, you may sometimes hear something like:

• ..., obwohl der Altbau sieht von außen schöner aus.

But that is colloquial and not the standard structure learners should use first. For normal correct German, use verb-final after obwohl.

Not with exactly the same meaning.

• lieber = rather / would rather
• am liebsten = most preferably / best of all
• eher = sooner / rather, often softer or more tentative

So:

• Wir würden lieber in einem Neubau wohnen = We would rather live in a new building.
• Wir würden am liebsten in einem Neubau wohnen = We would most like to live in a new building.
• Wir würden eher in einem Neubau wohnen = We would be more inclined to live in a new building.

In this sentence, lieber is the most natural choice for a direct comparison between Neubau and Altbau.