Learn Hardcore German: Später merkt er, dass sie sehr ehrgeizig ist, obwohl ihr Stil locker wirkt. - Later he realizes that she is very ambitious, although her style seems casual.

German main clauses normally have the finite verb in second position (the V2 rule).
That "second position" is counted in terms of elements, not single words.

So:

Später merkt er, ...
- Element 1: Später
- Element 2: merkt (verb)
- Element 3: er (subject)
Er merkt später, ...
- Element 1: Er
- Element 2: merkt (verb)
- Element 3: später

The word order changes the emphasis slightly:

Später merkt er, ... → Emphasis on the time: It’s later when he realizes...
Er merkt später, ... → More neutral; just says He realizes later...

In everyday speech, both are fine; the version with Später first sounds a bit more stylistically focused on the time aspect.

Why is dass spelled with ss and not das?

dass and das are two different words in German:

dass (with double s) is a subordinating conjunction meaning roughly “that” (introducing a clause):
- Er sagt, dass er müde ist. – He says that he is tired.
das (with one s) can be a relative pronoun, demonstrative pronoun, or article:
- Das ist gut. – That is good. (demonstrative)
- Das Buch, das ich lese, ist interessant. – The book that I’m reading is interesting. (relative pronoun)
- das Buch – the book (neuter article)

In your sentence, dass sie sehr ehrgeizig ist is a subordinate clause introduced by a conjunction, so you must use dass.

Why is the verb at the end in dass sie sehr ehrgeizig ist?

Because dass is a subordinating conjunction (Subjunktion), and in German, subordinating conjunctions send the finite verb to the end of the clause.

Pattern:

Main clause (V2):
Er merkt (verb in second position)
Subordinate clause with dass (verb-final):
..., dass sie sehr ehrgeizig ist.

Structure of the dass-clause:

Subject: sie
Predicate adjective: sehr ehrgeizig
Finite verb: ist (goes to the end)

This verb-final order also appears with other subordinating conjunctions like weil, obwohl, wenn, als, etc.

What is the function of obwohl here, and why does wirkt go to the end of its clause?

obwohl means “although / though / even though” and introduces a concessive subordinate clause – a clause that expresses something that contrasts with the main clause.

In obwohl ihr Stil locker wirkt, the structure is:

Subordinating conjunction: obwohl
Subject: ihr Stil
Predicate adjective: locker
Finite verb: wirkt (moved to the end)

As with dass, obwohl is a subordinating conjunction, so German word order rule applies: finite verb goes to the end in that clause.

The logic is:

Main information: He realizes she is very ambitious.
Concession/contrast: even though her style appears relaxed.

Why is it ihr Stil and not ihren Stil?

This is a question about case.

The noun Stil is masculine: der Stil.
ihr is a possessive determiner meaning “her”.

In ihr Stil, Stil is the subject of the obwohl-clause:

ihr Stil (subject, nominative)
wirkt (verb)
locker (predicate adjective)

For a masculine noun in nominative singular, the correct form is:

ihr Stil (not ihren Stil).

You would use ihren Stil if Stil were in the accusative and not the subject, for example:

Ich mag ihren Stil. – I like her style. (object → accusative)

What does wirkt mean here? How is it different from ist or scheint?

In this context, wirkt comes from wirken and means roughly “seems / appears / comes across as”.

ihr Stil wirkt locker ≈ her style seems/appears relaxed or her style comes across as relaxed.

Differences:

ist locker – is relaxed (states a fact more directly)
wirkt locker – appears relaxed (focus on the impression it makes)
scheint locker – seems relaxed (very close to wirkt, but wirken is often used for how someone or something comes across to others)

Example contrasts:

Sie ist locker. – She is relaxed. (statement of reality)
Sie wirkt locker. – She comes across as relaxed. (how she appears to others, regardless of what she’s really like)

What exactly does locker mean here? Is it the same as “relaxed”?

locker can mean several things depending on context: loose, easy-going, casual, relaxed.

In ihr Stil wirkt locker, it most naturally means something like:

casual / relaxed / easy-going in style, manner, or way of behaving.

Possible nuances:

ein lockerer Kleidungsstil – a casual style of clothing
ein lockerer Umgangston – an informal / easy-going tone
ein lockerer Typ – a laid-back person

So here, locker describes that her style (maybe the way she behaves, dresses, or works) doesn’t look strict, formal, or tense, but easy and relaxed.

How is ehrgeizig used? Is it always positive like “ambitious”?

ehrgeizig generally corresponds to “ambitious”, and like in English, it can be:

positive: motivated, driven, trying to achieve something
slightly negative: overly focused on success, possibly at the expense of other things

Examples:

Sie ist sehr ehrgeizig. – She is very ambitious.
Sein ehrgeiziger Plan ist schwer umzusetzen. – His ambitious plan is hard to implement.

In your sentence, sehr ehrgeizig suggests strong ambition, and the contrast with locker wirkt hints at: She looks laid-back, but in reality she’s very driven.

Why is ist (indicative) used and not sei (subjunctive) in dass sie sehr ehrgeizig ist?

German sometimes uses the subjunctive I/II (Konjunktiv) in reported speech, but here indicative is more natural.

Er merkt, dass sie sehr ehrgeizig ist.
→ He realizes/discovers that she is very ambitious.
- This is presented as a fact that he comes to understand. Indicative ist fits.

Subjunctive might appear in more formal reported speech:

Er sagt, sie sei sehr ehrgeizig. – He says she is very ambitious. (reported, possibly distanced)

Since merken, dass ... describes his own realization of something that is treated as true, the normal choice is ist, not sei.

Why are there commas before dass and before obwohl?

In German, subordinate clauses introduced by conjunctions such as dass, obwohl, weil, wenn, etc. must be separated from the main clause by commas.

Your sentence consists of:

Main clause: Später merkt er, ...
Subordinate clause 1: dass sie sehr ehrgeizig ist, ...
Subordinate clause 2 (inside the first): obwohl ihr Stil locker wirkt.

Punctuation:

Comma before dass:
Später merkt er, dass sie sehr ehrgeizig ist, ...
Comma before obwohl:
..., obwohl ihr Stil locker wirkt.

Each subordinate clause is marked off by commas. That’s standard German punctuation rules.

Could I leave out sehr and just say dass sie ehrgeizig ist? Does it change the meaning a lot?

Yes, you can absolutely say:

Später merkt er, dass sie ehrgeizig ist, obwohl ihr Stil locker wirkt.

The difference is only in degree:

ehrgeizig – ambitious
sehr ehrgeizig – very ambitious, strongly ambitious

Using sehr makes the contrast with locker a bit stronger:

She looks relaxed, but she’s actually *very ambitious.*

Without sehr, the contrast is still there, just a bit weaker. Both versions are natural and correct.