Die Mitarbeiterin muss jeden Koffer durchleuchten.

Yes. Mitarbeiterin is the feminine form and refers to a female employee. It is also the subject of the sentence, so it is in the nominative case. The nominative singular article for feminine nouns is die.

Related forms:

• der Mitarbeiter = male employee
• die Mitarbeiterin = female employee

Müssen is the dictionary form, but German verbs have to be conjugated. With die Mitarbeiterin = she, the correct present-tense form is muss.

Present tense of müssen:

• ich muss
• du musst
• er/sie/es muss
• wir müssen
• ihr müsst
• sie/Sie müssen

So die Mitarbeiterin muss means the employee must.

That is a normal pattern for this modal verb. In the singular present tense, müssen loses its umlaut:

• ich muss
• du musst
• er/sie/es muss

In the plural, the umlaut returns:

• wir müssen
• ihr müsst
• sie/Sie müssen

So this is something you learn as part of the verb’s conjugation.

Because muss is a modal verb. In a normal German main clause, the finite verb goes in second position. Here, the finite verb is muss, so it comes second.

The other verb, durchleuchten, stays in the infinitive and goes to the end:

• Die Mitarbeiterin = subject
• muss = finite verb
• jeden Koffer = object
• durchleuchten = infinitive at the end

This pattern is very common with modal verbs.

After a modal verb like muss, the second verb stays in the bare infinitive. It is not conjugated.

So you say:

• Die Mitarbeiterin muss jeden Koffer durchleuchten.

Not:

• Die Mitarbeiterin muss jeden Koffer durchleuchtet.

Without the modal, the verb would be conjugated:

• Die Mitarbeiterin durchleuchtet jeden Koffer.

Koffer is a masculine noun: der Koffer. In this sentence it is the direct object, so it is in the accusative case.

The word jeder changes in the masculine accusative singular:

• nominative: jeder Koffer
• accusative: jeden Koffer

That is why the sentence uses jeden Koffer.

Many masculine nouns in German do not change their ending in the accusative singular. Instead, the case is shown by the word before the noun.

Compare:

• der Koffer = nominative
• den Koffer = accusative
• jeder Koffer = nominative
• jeden Koffer = accusative

So the noun Koffer stays the same, while der / den / jeder / jeden changes.

Jeden Koffer can mean every suitcase or each suitcase. It emphasizes the suitcases one by one.

German could also say alle Koffer, but that sounds more like the whole group together:

• jeden Koffer = each/every suitcase individually
• alle Koffer = all suitcases as a group

Both are possible, but they are not exactly the same in nuance.

Yes. Durchleuchten is a single verb. In this sentence it means something like scan or X-ray. German often builds verbs by adding prefixes to a base verb, and learners usually need to memorize the full verb as one vocabulary item.

Without muss, the sentence would be:

• Die Mitarbeiterin durchleuchtet jeden Koffer.