Learn Hardcore German: Im Krankenwagen zeigt die Patientin ihre Versicherungskarte, damit die Daten aufgenommen werden können. - In the ambulance the patient shows her insurance card so that the data can be recorded.

in requires the dative case when it describes location (answering “where?”), so we need dem Krankenwagen (dative masculine).
In spoken and written German, in dem is almost always shortened to im.

So:

in dem Krankenwagen → im Krankenwagen (both mean “in the ambulance”).

Why is it dem Krankenwagen (masculine) and not der Krankenwagen or something else?

The base form is der Krankenwagen (nominative singular, masculine).

Because of the preposition in used for location, the noun goes into the dative:

Masculine dative singular of der is dem.
in + dem contracts to im.

Cases:

Nominative: der Krankenwagen (subject)
Dative: dem Krankenwagen → im Krankenwagen

What exactly does Krankenwagen mean? Is it the same as “ambulance”?

Yes, der Krankenwagen is the standard word for “ambulance” (the vehicle).

It’s a compound:

krank = sick / ill
Wagen = car / vehicle
→ literally “sick-vehicle”, i.e. ambulance.

Other common terms:

der Rettungswagen = emergency ambulance
der Notarztwagen = emergency doctor’s car (with a doctor on board)

Why is it die Patientin and not der Patient?

German marks grammatical gender directly on many nouns.

der Patient = male patient
die Patientin = female patient

The ending -in is the usual feminine ending for many professions and roles:

der Lehrer / die Lehrerin = (male / female) teacher
der Arzt / die Ärztin = (male / female) doctor

Here, the sentence is talking about a female patient, so die Patientin is used.

What case is die Patientin in, and why?

die Patientin is in the nominative case because it is the subject of the sentence — the person who does the action.

Wer zeigt die Versicherungskarte?
→ Die Patientin.
(Who shows the insurance card? The patient.)

So: subject → nominative → die Patientin.

What case is ihre Versicherungskarte, and how can I tell?

ihre Versicherungskarte is in the accusative case as the direct object (the thing being shown).

Wen oder was zeigt die Patientin?
→ ihre Versicherungskarte.
(Whom or what does the patient show? Her insurance card.)

For feminine nouns like die Versicherungskarte, the nominative and accusative look the same:

Nominative: die Versicherungskarte
Accusative: die Versicherungskarte

So you identify the case by the role in the sentence (direct object), not by a change in form.

Why is it ihre Versicherungskarte and not ihr Versicherungskarte?

Possessive pronouns in German agree with the gender, number, and case of the possessed noun, not with the owner.

Owner: die Patientin (feminine) — this does not affect the form.
Possessed noun: die Versicherungskarte
- feminine, singular, accusative.

For sie (she):

Feminine accusative singular: ihre

So:

ihre Versicherungskarte = her insurance card

Compare:

ihr Vater = her father (masc. nominative)
ihre Mutter = her mother (fem. nominative/accusative)
ihr Auto = her car (neuter nominative/accusative)

What does Versicherungskarte mean exactly?

die Versicherungskarte is your insurance card, specifically a health insurance card in this context.

It’s a compound:

Versicherung = insurance
Karte = card

So Versicherungskarte = insurance card (the card you present so that your insurance details can be read/recorded).

What does damit mean here, and how is it used?

damit introduces a subordinate clause of purpose and usually means “so that” or “in order that”.

Structure:

Main clause: Im Krankenwagen zeigt die Patientin ihre Versicherungskarte,
Purpose clause: damit die Daten aufgenommen werden können.

So the overall meaning is:

She shows the card so that the data can be recorded.

Grammar:

damit sends the finite verb to the end of the clause.
It can be used when the subject of the purpose clause is different or not the same person as in the main clause (here: the data vs. the patient).

Why is passive used: damit die Daten aufgenommen werden können instead of an active form?

German very often uses the impersonal passive where English would use “they” or “someone”.

Passive: damit die Daten aufgenommen werden können
= “so that the data can be recorded”
Rough active equivalent: damit man die Daten aufnehmen kann
= “so that they/one can record the data”

Using the passive focuses on the action and its possibility (the data being recorded), rather than on who does it (paramedics, staff, etc.).

What does aufgenommen mean in this context? Why not just genommen?

aufnehmen is a separable verb with several meanings. Here it means “to record / to take down / to register” (data, details).

die Daten aufnehmen = to record / register the data
die Personalien aufnehmen = to take down personal details

nehmen alone just means “to take” (physically take, accept, etc.), not “to record”.

Here, aufgenommen is the past participle of aufnehmen, used in the passive construction:

die Daten werden aufgenommen = the data are (being) recorded.

How does the verb order work in damit die Daten aufgenommen werden können?

In a subordinate clause with passive + modal verb, the verb cluster goes at the end in this order:

Past participle of the main verb: aufgenommen
Auxiliary infinitive for passive: werden
Finite verb (modal) at the very end: können

So you get:

damit die Daten aufgenommen werden können.

Pattern:

… damit [subject] [Partizip II] [Hilfsverb-Infinitiv] [Modal-Verb].

Example:

…, damit der Patient schnell behandelt werden kann.
(… so that the patient can be treated quickly.)

Why is the finite verb können at the very end of the damit-clause?

In German, subordinate clauses (introduced by damit, weil, dass, etc.) put the finite verb at the end.

Here, the finite verb is the modal können. Even though there are other verb forms in the clause (aufgenommen, werden), können carries the tense and person, so it must go last:

damit die Daten aufgenommen werden können
- aufgenommen (participle)
- werden (infinitive auxiliary)
- können (finite modal, therefore last)

Why are words like Krankenwagen, Patientin, Versicherungskarte, and Daten capitalized?

All nouns in German are capitalized, regardless of their position in the sentence.

So:

der Krankenwagen
die Patientin
die Versicherungskarte
die Daten

are all nouns, therefore they all start with a capital letter. This is a fixed rule in German spelling.