Vi kjøpte en gardinstang i går, men den er for lang til vinduet.

Yes, it can often be either, depending on the variety of Bokmål you use.

Gardinstang is traditionally a feminine noun, so many speakers say:

• ei gardinstang
• gardinstanga in the definite form

But in Bokmål, many feminine nouns can also be treated as common gender nouns, so you can also say:

• en gardinstang
• gardinstangen

In this sentence, en gardinstang is completely normal Bokmål.

It is a compound noun:

• gardin = curtain
• stang = rod / pole

So gardinstang literally means curtain rod.

Compound nouns are very common in Norwegian, and they are usually written as one word.

Kjøpte is the past tense of å kjøpe = to buy.

So:

• å kjøpe = to buy
• kjøper = buy / is buying
• kjøpte = bought
• har kjøpt = have/has bought

In Vi kjøpte en gardinstang i går, kjøpte means bought.

Because i går is the normal Norwegian expression for yesterday.

Literally, it looks like in yesterday, but you should learn it as a fixed expression:

• i går = yesterday
• i dag = today
• i morgen = tomorrow

So Vi kjøpte en gardinstang i går means We bought a curtain rod yesterday.

Because den refers back to en gardinstang, and that noun is common gender.

In Norwegian:

• den is used for common gender nouns
• det is used for neuter nouns

Since the sentence uses en gardinstang, the pronoun becomes den:

• en gardinstang → den
• et vindu → det if you were referring back to the window

So men den er for lang means but it is too long, with it referring to the curtain rod.

Here, for means too.

So:

• for lang = too long
• for stor = too big
• for dyr = too expensive

This is a very common point of confusion because Norwegian for does not always match English for.

In this sentence:

• den er for lang = it is too long

Because lang is a predicate adjective agreeing with den, which refers to a common gender singular noun.

Compare:

• Stangen er lang. = The rod is long.
• Vinduet er langt. = The window is long/wide in length.
  Here vinduet is neuter, so the adjective gets -t.

In your sentence, den refers to en gardinstang, so the correct form is:

• den er for lang

not den er for langt.

Because Norwegian normally uses til in the expression for lang til.

So:

• for lang til vinduet = too long for the window
• for stor til bilen = too big for the car
• for liten til jobben = too small for the job

This is just the natural Norwegian pattern. Even though English uses for, Norwegian usually uses til after adjectives like this.

Because vinduet is the definite form: the window.

• et vindu = a window
• vinduet = the window

The sentence refers to a specific window, probably one both speakers already know about, so Norwegian uses the definite form:

• til vinduet = for the window

This is very typical in Norwegian: definiteness is often shown by adding the article to the end of the noun.

Because Norwegian usually marks definiteness with a suffix on the noun.

Examples:

• en bil = a car
• bilen = the car
• et hus = a house
• huset = the house
• et vindu = a window
• vinduet = the window

So instead of a separate word like English the, Norwegian often adds the definite ending directly to the noun.

Because men means but, and here it connects two full clauses:

• Vi kjøpte en gardinstang i går
• den er for lang til vinduet

In standard Norwegian writing, a comma is normally used before men when it joins two independent clauses.

So the comma here is standard punctuation.

Because the two clauses talk about two different time frames:

• Vi kjøpte en gardinstang i går = the buying happened yesterday
• men den er for lang til vinduet = its being too long is true now

This is perfectly natural in both Norwegian and English. The action happened in the past, but the situation is still true in the present.

Yes. You could also say:

• I går kjøpte vi en gardinstang, men den er for lang til vinduet.

This puts more emphasis on yesterday.

Notice the word order:

• Vi kjøpte ... i går
• I går kjøpte vi ...

When a time expression like I går comes first in a main clause, the verb still has to stay in second position. This is the standard V2 word order rule in Norwegian.

So you say:

• I går kjøpte vi ...

not

• I går vi kjøpte ...

It is singular.

Here are the forms:

• et vindu = a window
• vinduet = the window
• vinduer = windows
• vinduene = the windows

So til vinduet means for the window, singular.

It can do both in different contexts.

In this sentence, den means it, because it refers back to the curtain rod:

• men den er for lang = but it is too long

But den can also be part of expressions meaning that, such as:

• den boken = that book

So the exact meaning depends on how it is used in the sentence. Here it is clearly a pronoun meaning it.

A speaker who prefers feminine forms might say:

• Vi kjøpte ei gardinstang i går, men den er for lang til vinduet.

Notice that den stays the same, because feminine nouns normally also take den as the pronoun in Bokmål.

If the noun were definite, that speaker might also say:

• gardinstanga instead of gardinstangen

So the sentence you were given is one normal Bokmål version, but there are other equally natural variants depending on gender preference.