Learn Hardcore German: Sie sagt, sie habe so stark bremsen müssen, weil ein Hund plötzlich über die Straße lief. - She says she had to brake so hard because a dog suddenly ran across the street.

In indirect / reported speech, German often uses Konjunktiv I to show that this is what someone claims, not what the narrator guarantees as fact:

Direct speech: „Ich habe so stark bremsen müssen …“
Indirect speech: Sie sagt, sie habe so stark bremsen müssen …

Using habe instead of hat marks the sentence as reported speech in a neutral way. It’s common in written German (news, reports, formal writing).

Can we also say „Sie sagt, sie hat so stark bremsen müssen …“?

Yes. In everyday spoken German, most people would actually say:

Sie sagt, sie hat so stark bremsen müssen, weil …

Using the indicative (hat) is very common in conversation and informal writing.

The difference:

Sie sagt, sie habe … – more formal / written, explicitly marked as reported speech.
Sie sagt, sie hat … – neutral, everyday language. Still understood as reported speech because of the verb sagt.

So both are grammatically fine; the version with habe just sounds more formal and “written-German-like”.

What exactly is the function of habe here? Is it the main verb?

No. Habe is the auxiliary verb for forming the present perfect (Perfekt) of the modal verb müssen:

Finite auxiliary: habe
Infinitives: bremsen müssen

Underlying structure (in normal indicative word order):

Ich habe so stark bremsen müssen.
→ auxiliary habe
- double infinitive bremsen müssen

In the sentence:

Sie sagt, sie habe so stark bremsen müssen, …

habe is:

In Konjunktiv I (habe instead of hat),
The only finite verb of that clause,
The auxiliary that “carries” tense and person for the infinitive group bremsen müssen.

Why is it bremsen müssen and not gemusst (e.g. „sie habe so stark bremsen gemusst“)?

This is the so‑called Ersatzinfinitiv (“substitute infinitive”).

With modal verbs (müssen, können, wollen, dürfen, sollen, mögen) plus another full verb, German normally avoids a past participle of the modal. Instead it uses the infinitive of the modal:

Correct: Ich habe bremsen müssen.
Very unusual / wrong in normal German: Ich habe bremsen gemusst.

So:

habe bremsen müssen = auxiliary + main verb + modal (double infinitive)
There is no form gemusst in this construction.

Why is the order bremsen müssen and not müssen bremsen?

In a double infinitive with a modal verb, the more “lexical” verb (the actual action) comes first, and the modal verb comes last:

bremsen müssen
arbeiten müssen
gehen wollen

Think of it as: “to brake” + “must”, “to work” + “must”, etc.

So:

… habe bremsen müssen ✔
… habe müssen bremsen ✖ (sounds wrong to native speakers)

Why is it so stark bremsen müssen? What does so stark add?

So stark is an intensifier: it means “so hard / so strongly” in this context.

bremsen müssen – had to brake
so stark bremsen müssen – had to brake so hard / so violently

Nuances:

stark with physical actions = strong / intense:
- stark bremsen, stark regnen, stark bluten
The so connects to the following weil-clause:
- She had to brake that hard because a dog suddenly crossed the street.

You could omit so stark grammatically, but you would lose the idea that it was an emergency / heavy braking.

Why is the verb at the end in „…, weil ein Hund plötzlich über die Straße lief.“?

Because weil is a subordinating conjunction. In German, subordinating conjunctions (weil, dass, obwohl, wenn, etc.) send the finite verb to the end of the clause:

Ein Hund lief plötzlich über die Straße. (main clause, verb in 2nd position)
…, weil ein Hund plötzlich über die Straße lief. (subordinate clause, verb final)

So the normal main‑clause word order gets changed by weil.

Why is it lief and not ist gelaufen?

Both are possible forms of the past in German:

lief – Präteritum (simple past) of laufen
ist gelaufen – Perfekt (present perfect) of laufen

In written German, the simple past for many verbs (including laufen) is quite normal, especially in narratives:

…, weil ein Hund plötzlich über die Straße lief. ✔ (very natural in writing)

In spoken German, people might more often say:

…, weil ein Hund plötzlich über die Straße gelaufen ist. ✔ (very natural in speech)

Meaning-wise here, there’s essentially no difference. It’s mostly a style / register choice.

Why is it über die Straße and not auf die Straße?

Because the dog is crossing the street, not just going onto it.

über die Straße = across the street (from one side to the other)
auf die Straße = onto the street (from somewhere else onto the surface of the street)

So:

Ein Hund lief plötzlich über die Straße.
→ A dog suddenly ran across the street.

If the dog simply jumped from the sidewalk onto the street and stayed there, you would use auf die Straße instead.

Why is it über die Straße (accusative) and not über der Straße (dative)?

Über is a two-way preposition (Wechselpräposition). With these prepositions:

Accusative = movement / direction towards / across / into something
Dative = location (no movement across a boundary)

Here we have movement across the street ⇒ accusative:

über die Straße – crossing the street (Akkusativ)

If you wanted to express a static position above the street, you’d say:

über der Straße – above the street (for example: Die Brücke hängt über der Straße.)

What is the function of plötzlich, and why is it placed where it is?

Plötzlich means “suddenly” and describes how / under what circumstances the dog ran across the street.

Position:

…, weil ein Hund plötzlich über die Straße lief.

Adverbs of manner / time / degree like plötzlich are quite flexible, but this position is very typical:

Subject: ein Hund
Adverb: plötzlich
Rest of predicate: über die Straße lief

You could also say:

…, weil ein Hund über die Straße lief, plötzlich. – possible, but stylistically odd here.
…, weil plötzlich ein Hund über die Straße lief. – also possible; here plötzlich highlights the surprise.

The chosen order is the most neutral and natural.

Why is there a comma after „Sie sagt,“?

Because what follows is a dependent clause that functions as the object of sagt (what she says):

Sie sagt, [sie habe so stark bremsen müssen, weil …].

German spelling rules require a comma before all finite clauses, especially after reporting verbs (sagen, meinen, glauben, fragen, …), whether or not dass is present.

You could also write:

Sie sagt, dass sie so stark bremsen musste, weil …

Here too, there must be a comma before dass.

Could we rephrase this using musste bremsen instead of habe bremsen müssen? Would that change the meaning?

Yes, and the meaning would stay essentially the same. For example:

Sie sagt, sie musste so stark bremsen, weil ein Hund plötzlich über die Straße lief.

Differences:

musste bremsen – Präteritum (simple past) of müssen; very common and neutral in both spoken and written German.
habe bremsen müssen – Perfekt with double infinitive; here put into Konjunktiv I (habe) for indirect speech.

In content, both describe the same past event: she had to brake hard. The original sentence uses the Perfekt + Konjunktiv I to stick closely to what she (supposedly) said, in a more “reported speech” style.