Den viktigaste ingrediensen i soppan är lök.

Because ingrediens is an en-word (common gender) in Swedish.

• en ingrediens
• den viktigaste ingrediensen

If the noun were a det-word (neuter), you would use det instead.

So den agrees with ingrediens, not with soppa or lök.

This is a very common Swedish pattern called double definiteness.

When you have:

• a definite noun
• with an adjective before it

Swedish usually marks definiteness twice:

1. with a definite article before the adjective: den
2. with the definite ending on the noun: ingrediens-en

So:

• ingrediensen = the ingredient
• den viktigaste ingrediensen = the most important ingredient

English only marks definiteness once, but Swedish often does it twice in this structure.

Viktigaste is the superlative form of viktig.

The forms are:

• viktig = important
• viktigare = more important
• viktigast = most important

Before a definite noun, Swedish normally uses viktigaste:

• den viktigaste ingrediensen

Compare:

• Den här ingrediensen är viktigast. = This ingredient is most important.
• Den viktigaste ingrediensen... = The most important ingredient...

So viktigaste is the form you expect before a definite noun phrase.

Because soppan means the soup.

After a preposition like i (in), Swedish still uses the definite form when you mean a specific thing:

• i soppan = in the soup
• i huset = in the house
• på bordet = on the table

Here, it is a particular soup, so Swedish says i soppan, not just i soppa.

Here lök is being used as a material/substance/category word, not as one specific onion.

So:

• lök = onion / onions / onion as an ingredient
• en lök = an onion
• löken = the onion

In sentences like this, Swedish often leaves out the article after är when talking about what something is made of or what the key ingredient is:

• Huvudingrediensen är lök.
• Det är guld.
• Soppan innehåller potatis.

So lök here means something like onion in a general ingredient sense.

Yes, but the meaning changes a little.

• ...är lök = onion is the main ingredient, in a general sense
• ...är löken = the onion is the main ingredient, referring to a specific onion or a specific onion component already known from context

In most neutral contexts about ingredients, lök sounds more natural.

The whole phrase Den viktigaste ingrediensen i soppan is the subject.

You can divide the sentence like this:

• Den viktigaste ingrediensen i soppan = subject
• är = verb
• lök = subject complement / predicative expression

So the sentence structure is basically:

[subject] + [verb] + [what the subject is]

Yes. This is the standard order for a simple statement:

• subject + verb + complement

So:

• Den viktigaste ingrediensen i soppan
  • är
    • lök

Very normal.

If something else were moved to the front, Swedish would still keep the verb in second position, for example:

• I soppan är den viktigaste ingrediensen lök.

That sounds more marked or contrastive, but it is still grammatical.

These are two vowels English speakers often notice right away:

• ä in är sounds somewhat like the vowel in British English there or fair, but not exactly.
• ö in lök has no exact English equivalent. It is a rounded front vowel. A rough starting point is to say something like lay or bird while rounding your lips more.

Very rough pronunciation guide:

• är ≈ ehr
• lök ≈ something like lurk/lake with rounded lips — not a perfect English match

You will hear these sounds a lot in Swedish, so they are worth practicing early.

Because viktigaste describes ingrediensen, not lök.

The phrase is:

• Den viktigaste ingrediensen = the most important ingredient

Then the sentence says what that ingredient is:

• ...är lök

So the adjective belongs inside the subject phrase and agrees with ingrediensen conceptually, not with the word after är.

Yes, in ingredient language it can be quite general.

Just like English can say:

• The main ingredient is onion

Swedish can say:

• Den viktigaste ingrediensen är lök

This does not necessarily mean exactly one onion. It means onion as an ingredient/category. Context tells you whether that means onion in general, chopped onion, a lot of onion, and so on.