Det formstøpte høreapparatet er ødelagt. Ikke desto mindre virker volumkontrollen.

This is a very common feature of Norwegian called double definiteness.

When a noun is definite and has an adjective before it, Norwegian usually marks definiteness twice:

• with den/det/de before the adjective
• and with the definite ending on the noun itself

So:

• høreapparatet = the hearing aid
• det formstøpte høreapparatet = the custom-molded hearing aid

Because høreapparat is a neuter noun, the preposed article is det.

Compare:

• et formstøpt høreapparat = a custom-molded hearing aid
• det formstøpte høreapparatet = the custom-molded hearing aid

Because the adjective is placed before a definite noun.

In Norwegian, adjectives usually take the -e form when they come before a definite noun:

• et formstøpt høreapparat = indefinite
• det formstøpte høreapparatet = definite

So formstøpte is the expected form in this structure.

This word is originally a past participle from a verb, but here it behaves like an adjective.

Formstøpt literally suggests something that has been molded to a shape or cast in a form.

In this sentence, a natural English equivalent is often:

• custom-molded
• molded
• shaped to fit

For a hearing aid, custom-molded is especially natural, since such devices are often made to fit the ear.

It is a compound noun:

• høre = hearing
• apparat = device / apparatus
• -et = the definite singular ending for a neuter noun

So:

• et høreapparat = a hearing aid
• høreapparatet = the hearing aid

Compound nouns are very common in Norwegian, and the whole thing is written as one word.

Here er is the present tense of å være (to be), and ødelagt describes the state of the hearing aid.

So the structure is:

• X er ødelagt = X is broken / damaged

This is a very common pattern in Norwegian:

• Bilen er ødelagt. = The car is broken.
• Telefonen er ødelagt. = The phone is broken.

Even though ødelagt comes from the verb å ødelegge (to destroy / damage / ruin), in sentences like this it functions like an adjective.

Ikke desto mindre means nevertheless, nonetheless, or all the same.

It is a fixed expression and sounds a bit more formal or written than some other options.

A more everyday alternative is often:

• likevel

So these are very similar:

• Ikke desto mindre virker volumkontrollen.
• Volumkontrollen virker likevel.

Both mean roughly the same thing, but ikke desto mindre sounds more formal or literary.

This is because Norwegian is a verb-second language in main clauses.

That means the finite verb usually comes in the second position, no matter what comes first.

Here, the sentence starts with the adverbial expression:

• Ikke desto mindre

So the verb must come next:

• Ikke desto mindre virker volumkontrollen.

Then comes the subject:

• volumkontrollen

Compare:

• Volumkontrollen virker.
  Here the subject comes first, so the verb comes second.

• Likevel virker volumkontrollen.
  Here likevel comes first, so the verb still comes second.

This word order is very important in Norwegian.

Yes. In this sentence, virker means works or functions.

The verb is å virke, which can mean several things depending on context, such as:

• to work / function
• to seem / appear
• to have an effect

Here the meaning is clearly functions:

• volumkontrollen virker = the volume control works

So even though the hearing aid is broken, the volume control still functions.

Because kontroll is a common-gender noun, not a neuter noun.

So:

• en kontroll = a control
• kontrollen = the control

When it becomes part of the compound volumkontroll, it keeps the gender of the final element, which is normal in Norwegian compounds:

• en volumkontroll
• volumkontrollen

So the definite form is -en, not -et.

It is correct and understandable, but it sounds a bit formal, especially because of ikke desto mindre.

A more everyday version might be:

• Det formstøpte høreapparatet er ødelagt, men volumkontrollen virker fortsatt.
• Det formstøpte høreapparatet er ødelagt. Likevel virker volumkontrollen.

So the original sentence is fine, but it has a slightly more polished or written style.

Yes, but the meaning and structure are different.

• det formstøpte høreapparatet = the custom-molded hearing aid
  Here formstøpte is part of the noun phrase and identifies which hearing aid you mean.

• høreapparatet er formstøpt = the hearing aid is custom-molded
  Here formstøpt is in the predicate and tells you something about the hearing aid.

So both are possible, but they are used in different sentence patterns.