Learn Hardcore German: Alle alten Termine müssen im Kalender durchgestrichen werden. - All old appointments must be crossed out in the calendar.

Alle behaves like a "der-word" (like die, diese, jene, solche, welche, manche).
After such words, adjectives take the weak declension, which in the plural is always -en, regardless of case.

So:

alle alten Termine = all old appointments
- alle = determiner (like "all")
- alten = adjective with -en ending (weak declension)
- Termine = plural noun

You cannot say alle alte Termine, because alte would be the strong ending; that is used without a der-word (e.g. alte Termine on its own, or after viele, wenige in some patterns).

What case is Termine in here, and why?

Grammatically, Termine is nominative plural.

It is the subject of the passive sentence:
- Alle alten Termine = subject
- müssen … durchgestrichen werden = passive verb phrase

In the corresponding active sentence, Termine would be accusative:

Jemand muss alle alten Termine im Kalender durchstreichen.
(Someone must cross out all the old appointments in the calendar.)

When you turn that into passive:

Alle alten Termine müssen im Kalender durchgestrichen werden.

The former accusative object (alle alten Termine) becomes the subject (nominative) of the passive sentence.

Note: in the plural, nominative and accusative look the same (die/alle alten Termine), which can make this less obvious.

How does the verb structure müssen … durchgestrichen werden work?

You have three important elements:

müssen – modal verb (finite, conjugated: müssen for "sie" plural)
durchgestrichen – past participle of durchstreichen
werden – infinitive of werden, used to build the passive

In German word order with a modal + passive:

The modal verb is in second position, conjugated:
- Alle alten Termine müssen …
The other verbs go to the end of the clause as infinitive/participle cluster:
- … durchgestrichen werden.

So the pattern is:

Subj + müssen + [rest of sentence] + Participle + werden

Compare:

Without passive, just modal + infinitive:
- Wir müssen alle alten Termine im Kalender durchstreichen.
With passive + modal:
- Alle alten Termine müssen im Kalender durchgestrichen werden.

Why is the past participle durchgestrichen and not something like gestricht?

Because the base verb is durchstreichen, a separable-prefix verb:

Infinitive: durchstreichen
Present: ich streiche … durch, er streicht … durch
Simple past: er strich … durch
Perfect: er hat … durchgestrichen

For separable-prefix verbs:

The prefix (durch-) moves to the end in main clauses:
- Ich streiche den Termin im Kalender durch.
The past participle gets ge- between the prefix and the stem:
- durch + ge + strichen → durchgestrichen

Gestricht is not a valid form; the correct participle of streichen is gestrichen, and with the separable prefix it becomes durchgestrichen.

What exactly does durchgestrichen werden mean compared to just gestrichen werden?

durchstreichen = to cross out, to strike through (visibly draw a line through text/an entry)
streichen by itself is more general: to paint, to cancel, to cut (from a list)

So:

durchgestrichen werden = to be crossed out (with a line through it)
gestrichen werden = to be cancelled/removed (context-dependent, not necessarily visually crossed out)

In a calendar context:

durchgestrichen werden emphasizes the physical action in the calendar: drawing a line through old appointments.
gestrichen werden would mean they’re cancelled or removed, but doesn’t say how (deleted, not happening, etc.).

Why is it im Kalender and not something like im Kalendarium or aus dem Kalender?

im Kalender is the most natural everyday expression:

im = contraction of in dem (in + the, dative)
Kalender = calendar (book, app, or wall calendar)

in + dative here expresses location: in the calendar, where the appointments are written.

Alternatives:

aus dem Kalender streichen – literally to strike from the calendar (focus on removing them from the list)
im Terminkalender – in the appointment calendar (more specific)
aus dem Terminkalender streichen – from the appointments calendar

In your sentence, im Kalender focuses on where the crossing-out happens, not so much on the idea of removal from a list.

Why do we use müssen here and not sollen or dürfen?

Each modal verb expresses a different nuance:

müssen = must / have to → strong necessity or obligation
sollen = should / supposed to → recommendation, instruction, weaker obligation, or reporting someone else’s wish
dürfen = may / be allowed to → permission

In Alle alten Termine müssen im Kalender durchgestrichen werden:

müssen indicates a firm requirement: it is necessary, not just advisable.
With sollen:
- Alle alten Termine sollen im Kalender durchgestrichen werden.
- This feels more like an instruction or guideline, less strict than müssen.

So müssen fits if, for example, this is a rule in an office procedure.

Why is müssen plural here and how do we know which form to use?

Müssen must agree with the subject:

Subject: Alle alten Termine → clearly plural
So we use sie (Plural) müssen

Quick overview of müssen in the present tense:

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

Since Termine is plural, we conjugate as for sie (Plural): müssen.

If the subject were singular:

Der alte Termin muss im Kalender durchgestrichen werden.
- Der alte Termin = singular → muss

Could this sentence be turned into an active sentence, and how would that change the feel?

Yes. A natural active version would be:

Wir müssen alle alten Termine im Kalender durchstreichen.
- We must cross out all the old appointments in the calendar.

Or with an unspecified subject:

Man muss alle alten Termine im Kalender durchstreichen.
- You/one must cross out all the old appointments in the calendar.

Difference in feel:

Passive (original):
- Alle alten Termine müssen im Kalender durchgestrichen werden.
- Focuses on the appointments and what must happen to them; doer is irrelevant or unknown.
Active:
- Focuses on who has to perform the action (wir, man, etc.).

German often uses the passive or man when the agent is not important.

Is the tense here strictly present, or can it refer to the future too?

Grammatically, it’s present tense:

müssen is in the present: müssen

But in German, the present tense is often used with a future meaning, especially for:

rules
schedules
planned procedures

So Alle alten Termine müssen im Kalender durchgestrichen werden can mean:

All old appointments *must (now/always) be crossed out in the calendar.* (general rule)
Or, in context, All the old appointments *will have to be crossed out in the calendar (soon).* (near future)

To make the future more explicit, you could say:

Alle alten Termine werden im Kalender durchgestrichen werden müssen.
(grammatically correct but heavy; usually avoided in favor of simple present + context)

So the given sentence is present in form, but can cover present or future depending on context.