Nach dem Vortrag bleibt eine Zuhörerin noch im Raum, ruhig wartend, bis die Sprecherin Zeit hat.

The preposition nach always takes the dative case when it means after (in time).

• der Vortrag (the lecture) – nominative
• nach + Dativ → dem Vortrag

So you must say:

• nach dem Vortrag = after the lecture

Using nach der Vortrag would be wrong because der is the nominative or feminine dative; Vortrag is masculine, so the correct dative article is dem.

Here noch means still (or remaining), emphasizing that she stays on while others presumably leave.

Nuances:

• Sie bleibt im Raum. – She stays in the room. (neutral)
• Sie bleibt noch im Raum. – She still stays / She remains in the room (others may have gone).

Other common meanings of noch:

• noch ein Kaffee – another coffee
• noch nicht – not yet

In this sentence, understand it as still / remaining / staying on.

The ending -in marks a female person doing the activity:

• der Zuhörer – (male) listener
• die Zuhörerin – female listener
• der Sprecher – (male) speaker
• die Sprecherin – female speaker

So:

• eine Zuhörerin – a (female) listener
• die Sprecherin – the (female) speaker

If you wanted to talk about a male listener and speaker, you’d say:

• ein Zuhörer
• der Sprecher

And for mixed or unspecified gender in more traditional usage, Zuhörer / Sprecher often functions as a generic masculine, though modern German increasingly uses gender-inclusive forms (like Zuhörerinnen und Zuhörer or with a *: Zuhörer*innen).

im is the contracted (shortened) form of in dem:

• in + dem Raum → im Raum

This contraction is very common and usually more natural in speech and writing. Both are grammatically correct:

• Sie bleibt in dem Raum.
• Sie bleibt im Raum.

They mean the same thing here. Contextually, im Raum just sounds smoother and is the default choice.

The preposition in can take either dative or accusative, depending on the meaning:

• Dative = location (where something is)
• Accusative = direction/movement (where something is going)

Here we have a location (she is staying in the room), so we use dative:

• Wo bleibt sie? – im Raum (dative)

If it were movement into the room, then accusative:

• Sie geht in den Raum. – She goes into the room. (accusative)

ruhig wartend is a participle construction describing how she stays in the room. It’s like a short relative clause or like an English -ing phrase:

• ruhig wartend ≈ while waiting calmly / quietly waiting

More explicitly you could say:

• …, während sie ruhig wartet, … – …while she waits calmly…

But German often uses a Partizip I (present participle) to make things more compact:

• lachend – laughing
• lesend – reading
• wartend – waiting

Combined with an adverb:

• ruhig wartend – waiting calmly

So ruhig wartend modifies the subject eine Zuhörerin and tells us in what manner she remains in the room.

When a participle is used directly in front of a noun, like an adjective, it normally takes adjective endings:

• die ruhig wartende Zuhörerin – the quietly waiting listener

But in your sentence, ruhig wartend does not stand before a noun. It stands in a loose participle phrase, separated by commas:

• Eine Zuhörerin bleibt im Raum, ruhig wartend, bis …

Here it behaves more like an adverbial phrase (describing how she stays), not like an adjective before a noun, so it stays in its base form:

• sie bleibt dort, ruhig wartend
• sie sitzt da, lesend und nickend

No -e ending is needed in this position.

Literally:

• bis – until
• die Sprecherin – the (female) speaker
• Zeit hat – has time

So: until the speaker has time.

In German it’s very natural to just say someone hat Zeit (= has time), and the context usually implies for what. English often adds time for her / time for questions / time to talk to her, but German can leave it unstated:

• Ich habe keine Zeit. – I don’t have time.
• Hast du später Zeit? – Do you have time later?

In a fuller version, you could say:

• …, bis die Sprecherin Zeit hat, mit ihr zu sprechen.
  – …until the speaker has time to speak with her.

But that last part is obvious from context, so the shorter bis die Sprecherin Zeit hat is natural.

German main clauses follow the V2 rule: the finite verb (here: bleibt) must be in second position, but “second” means second element, not necessarily second word.

In this sentence:

1. Nach dem Vortrag – this whole phrase is one element (a prepositional phrase of time).
2. bleibt – the finite verb in 2nd position.
3. eine Zuhörerin… – subject and the rest of the clause follow.

So the structure is:

• [Nach dem Vortrag] [bleibt] [eine Zuhörerin noch im Raum, …]

If you move the subject to the front instead:

• Eine Zuhörerin bleibt nach dem Vortrag noch im Raum, …

The verb bleibt is still in second position.

Yes, you could write:

• Nach dem Vortrag bleibt eine Zuhörerin noch im Raum und wartet ruhig, bis die Sprecherin Zeit hat.

Differences:

• ruhig wartend – more compact, a bit more literary or written style. It fuses the description into a participle phrase.
• und wartet ruhig – more neutral and conversational, two clear actions joined with und.

Both are correct. The original with ruhig wartend sounds slightly more descriptive and stylistically elevated.

This reflects what is known vs. new in the context:

• eine Zuhörerin – a listener; she is being introduced for the first time, so we use the indefinite article.
• die Sprecherin – the speaker; this is a specific, identifiable person (the one who just gave the lecture), so we use the definite article.

In English you might also say:

• After the lecture, *a listener stays in the room… until the speaker has time.*

Using die Sprecherin assumes both speaker and listener already know who that speaker is (e.g., the one who just gave the talk).

Vortrag usually means:

• lecture, talk, or presentation given to an audience.

So depending on context, it can be translated as:

• a university lecture
• a conference talk
• a business presentation

German doesn’t distinguish as strictly between lecture and presentation as English does. Vortrag covers most formal spoken talks with an audience. For a more obviously business-style presentation, you might also see Präsentation, but Vortrag is very common and natural here.