Soppan blev värmd igen i mikrovågsugnen.

Because Swedish usually puts the definite article on the end of the noun.

• en soppa = a soup
• soppan = the soup

So -n is the definite ending here. The full ending appears as -an because the base word is soppa.

If there is an adjective, Swedish often uses both a separate article and the ending:

• den varma soppan = the warm soup

That is a very common question. Bli does normally mean become, and blev is its past tense.

But Swedish also uses bli + past participle to make a passive meaning:

• blev värmd = was heated / got heated

So the structure is literally close to became heated, but in natural English it is usually translated as was heated or got heated.

Because the participle agrees with the noun it describes.

Here, soppan comes from en soppa, and en-words take the common-gender singular form värmd.

Compare:

• en soppa → soppan blev värmd
• ett ägg → ägget blev värmt
• grönsakerna → grönsakerna blev värmda

So värmd matches the gender and number of soppan.

Yes. This is the bli-passive.

The sentence is active in structure only in the sense that it uses the verb bli, but the meaning is passive: the soup receives the action.

• Active: Någon värmde soppan igen i mikrovågsugnen.
  = Someone heated the soup again in the microwave.

• Passive: Soppan blev värmd igen i mikrovågsugnen.
  = The soup was heated again in the microwave.

Yes. That is also correct.

Swedish has two common ways to make the passive here:

1. bli-passive: blev värmd
2. s-passive: värmdes

So these are both possible:

• Soppan blev värmd igen i mikrovågsugnen.
• Soppan värmdes igen i mikrovågsugnen.

They are very close in meaning. A simple way to think about the difference is:

• blev värmd often emphasizes the event or change of state
• värmdes is shorter and very common as a straightforward passive

This is an important distinction.

• blev värmd focuses on the action/event: the soup underwent heating
• var värmd describes a state: the soup was in a heated/warm condition

Compare:

• Soppan blev värmd igen.
  = The soup was heated again.

• Soppan var redan värmd.
  = The soup was already heated.

So blev points to something happening, while var points more to how something was.

Because igen usually comes after the main lexical verb or participle in a sentence like this.

So:

• Soppan blev värmd igen i mikrovågsugnen.

is natural.

Here blev is the finite auxiliary-like verb, and värmd carries the main lexical meaning. The adverb igen fits naturally after that verbal idea: heated again.

A version like Soppan blev igen värmd ... sounds unnatural in normal modern Swedish.

It is a compound noun, which is extremely common in Swedish.

It breaks down like this:

• mikrovåg = microwave
• ugn = oven
• mikrovågsugn = microwave oven
• mikrovågsugnen = the microwave oven

The -s- in the middle is a linking sound that often appears in compounds.

So Swedish packs the idea into one word where English uses two.

Because the soup is heated inside the microwave, not on top of it.

• i mikrovågsugnen = in the microwave
• på mikrovågsugnen = on the microwave

So i is the normal preposition here.

Yes, it could, depending on context.

• i mikrovågsugnen = in the microwave / in the microwave oven
  This usually refers to a specific, understood microwave.

• i en mikrovågsugn = in a microwave oven
  This sounds more general or less specific.

In everyday situations, the definite form is very natural because people usually mean a particular microwave that is already known from context.

Often, yes. In everyday Swedish, many speakers would naturally say something like:

• Soppan värmdes upp igen i mikron.

That said, värma by itself is still correct. It simply means heat. Adding upp often makes it sound a bit more like heat up / warm up in everyday speech.

Also, in casual spoken Swedish, mikron is very common instead of mikrovågsugnen.

So all of these are possible, depending on style:

• Soppan blev värmd igen i mikrovågsugnen.
• Soppan värmdes igen i mikrovågsugnen.
• Soppan värmdes upp igen i mikron.

They are all understandable, but the last one sounds especially natural in casual conversation.