Trykktesten virket unødvendig, men var tvert imot viktig.

Trykktesten is the definite singular form of trykktest.

• en trykktest = a pressure test
• trykktesten = the pressure test

Norwegian often uses the definite form when talking about a specific thing already known from context. The ending -en is the usual definite ending for many masculine nouns.

So:

• trykktest = base form
• trykktesten = the pressure test

Yes. Trykktesten is built from the compound noun trykktest:

• trykk = pressure
• test = test

Together, trykktest means pressure test. Then the definite ending -en is added:

• trykktest → trykktesten

Compound nouns are very common in Norwegian, just as in English, but Norwegian usually writes them as one word.

They are two different past-tense verbs with different meanings:

• virket is the past tense of å virke = to seem / to appear
• var is the past tense of å være = to be / was

So the sentence contrasts appearance and reality:

• it seemed unnecessary
• but was on the contrary important

That contrast is exactly why both verbs are used.

Because the subject is understood to be the same as in the first clause: trykktesten.

Full version:

• Trykktesten virket unødvendig, men trykktesten var tvert imot viktig.

In natural Norwegian, just like in English, you usually omit the repeated subject when it is obvious:

• The pressure test seemed unnecessary, but was actually important.

So this is perfectly normal and natural.

Tvert imot means on the contrary, quite the opposite, or actually the reverse.

It is a fixed expression used to strongly contradict what came before.

In this sentence:

• virket unødvendig = seemed unnecessary
• tvert imot viktig = on the contrary, important

So it does more than just add contrast; it reverses the expectation.

Here they are predicate adjectives, used after verbs like å være and å virke.

In this sentence:

• virket unødvendig
• var ... viktig

The noun trykktesten is singular and definite, but predicate adjectives usually stay in their basic form unless grammar requires something else.

Compare:

• en viktig test = an important test

• testen er viktig = the test is important

• en unødvendig test = an unnecessary test
• testen virker unødvendig = the test seems unnecessary

So the lack of extra endings here is normal.

Yes. This is standard Norwegian main-clause word order:

• subject
  • verb
    • complement

So:

• Trykktesten = subject
• virket = verb
• unødvendig = adjective complement

Norwegian is a V2 language, which means the finite verb usually comes in the second position in main clauses. Since the subject comes first here, the verb naturally comes right after it.

Men means but.

It connects the two clauses and signals contrast:

• Trykktesten virket unødvendig
• men var tvert imot viktig

So men introduces the second idea, which corrects or opposes the first one.

Yes, that would also be grammatical:

• Trykktesten virket unødvendig, men den var tvert imot viktig.

Using den makes the subject explicit again. The original sentence sounds slightly more compact and elegant because the repeated subject is omitted.

Both are natural, but the version without den is very common when the subject is clearly the same.

It can mean different things depending on context.

From å virke, common meanings include:

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

In this sentence, it clearly means seemed because it is followed by an adjective:

• virket unødvendig = seemed unnecessary

If it meant worked, the structure would usually be different, for example:

• Maskinen virket ikke. = The machine did not work.

It would be:

Trykktesten virker unødvendig, men er tvert imot viktig.

Changes:

• virket → virker
• var → er

So:

• past: virket ... var
• present: virker ... er

Yes, but some placements sound more natural than others.

In your sentence, var tvert imot viktig is very natural. You can also see tvert imot used more independently, for example:

• Det var ikke unødvendig. Tvert imot var det viktig.

Here it introduces a whole new clause more emphatically.

So tvert imot is flexible, but in this sentence its placement is especially smooth and idiomatic.