Das Seminar ist voll, aber die Teamleiterin bleibt ruhig, und die Zuhörer stellen viele Fragen zum Vortrag.

Every German noun has a fixed grammatical gender that you simply have to learn with the word.

• Seminar is grammatically neuter, so it takes the article das in the nominative singular: das Seminar.
• Other examples of neuter nouns: das Auto, das Kind, das Zimmer.

You cannot change the article based on the real-world gender (a seminar has no natural gender); it always stays das Seminar.

In ist voll, voll is a predicate adjective, coming after a form of sein (ist).
Predicate adjectives in German normally have no ending:

• Das Zimmer ist groß.
• Die Aufgaben sind schwer.

Adjective endings appear when the adjective directly precedes a noun:

• ein volles Seminar (a full seminar)
• ein großes Zimmer (a big room)

aber is a coordinating conjunction meaning but, expressing contrast:

• Das Seminar ist voll, aber die Teamleiterin bleibt ruhig.
  → The seminar is full, but the team leader stays calm.

sondern is used after a negation, meaning but rather / but instead:

• Das Seminar ist nicht leer, sondern voll.
  → The seminar is not empty, but rather full.

In your sentence there is no negation before aber, so aber (not sondern) is correct.

German must use a comma before aber when it connects two main clauses:

• Das Seminar ist voll, aber die Teamleiterin bleibt ruhig.

With und (and oder) between main clauses, the comma is optional under current rules. In your sentence:

• ..., aber die Teamleiterin bleibt ruhig, und die Zuhörer stellen viele Fragen ...

Here und connects two full main clauses:

1. die Teamleiterin bleibt ruhig
2. die Zuhörer stellen viele Fragen

So the comma before und is allowed and often used for clarity, but you could also write:

• ..., aber die Teamleiterin bleibt ruhig und die Zuhörer stellen viele Fragen ...

Teamleiterin is a feminine noun meaning (female) team leader.
It’s formed from:

• Team (team)
• Leiter (leader, manager)
• plus the feminine ending -in → Leiterin (female leader)

So:

• der Teamleiter = male team leader
• die Teamleiterin = female team leader

The ending -in (plural -innen) is the regular feminine ending for many job titles and roles:

• der Lehrer / die Lehrerin (teacher)
• der Student / die Studentin (student)

Both are possible, but they have slightly different nuances:

• ist ruhig = is calm (a simple description of her state)
• bleibt ruhig = stays/remains calm (emphasizes that she continues to be calm, even though the situation could make her nervous)

In a context where the seminar is full (potentially stressful), bleibt ruhig underlines that she does not lose her calm.

Yes, bleiben often works similarly to sein or werden as a linking verb. It connects the subject to a state or characteristic:

• Sie bleibt ruhig. → She stays/remains calm.
• Er bleibt freundlich. → He remains friendly.

In such cases, the adjective that follows (ruhig) also appears without an ending, just like after sein:

• Sie ist ruhig.
• Sie bleibt ruhig.

die Zuhörer means the listeners or the audience members – people who are listening to the talk.
Here, Zuhörer is plural, nominative case: die Zuhörer.

The singular is:

• der Zuhörer = (male) listener
• die Zuhörerin = (female) listener

For a group in general, you can also use das Publikum (the audience), which is grammatically singular but refers to a group of people.

In German, the usual expression is Fragen stellen (literally: to pose questions), not Fragen fragen.
So you say:

• Die Zuhörer stellen viele Fragen. → The listeners ask many questions.
• Darf ich Ihnen eine Frage stellen? → May I ask you a question?

The verb fragen is normally used with a person or about something, not with Fragen as an object:

• Ich frage den Lehrer. → I ask the teacher.
• Ich frage nach dem Weg. → I ask for directions.

But ich stelle eine Frage or ich stelle viele Fragen is the natural way to say I ask a question / many questions.

viele Fragen is accusative plural, because it’s the direct object of the verb stellen:

• Wer stellt was?
  
  • Die Zuhörer (subject, nominative)
  • stellen viele Fragen (direct object, accusative)

In the accusative plural with no article, viele has no extra ending:

• Ich sehe viele Leute.
• Wir kaufen viele Bücher.

You would see vielen in the dative plural, e.g.:

• mit vielen Fragen
• an vielen Seminaren teilnehmen

zum Vortrag means about the lecture / about the talk (literally: to the lecture).

zum is a contraction of zu dem:

• zu (to, about) + dem (dative singular of der for masculine/neuter nouns) = zum

Vortrag (lecture/talk) is masculine:

• Nominative: der Vortrag
• Dative: dem Vortrag → zum Vortrag

The preposition zu always takes the dative:

• zum Arzt (zu dem Arzt) – to the doctor
• zur Schule (zu der Schule) – to school

In this context, Fragen zum Vortrag is a very common phrase meaning questions about the content of the talk/lecture.

Yes, Fragen über den Vortrag is grammatically correct and understandable.
However, Fragen zum Vortrag is more idiomatic and more common in German in this context.

Nuance:

• Fragen zum Vortrag: very standard collocation for questions concerning / related to the lecture.
• Fragen über den Vortrag: can sound slightly more like questions about the lecture as a topic, but in everyday language many people would not feel a big difference.

If you’re unsure, Fragen zum Vortrag is the safest and most natural choice.

In main clauses, the German rule is verb in second position (V2), not at the very end:

• Das Seminar ist voll.
• Die Teamleiterin bleibt ruhig.
• Die Zuhörer stellen viele Fragen.

aber and und here connect main clauses, so the normal main-clause word order stays:

• ..., aber die Teamleiterin bleibt ruhig, und die Zuhörer stellen viele Fragen ...

Verb-final word order (verb at the end) is typical of subordinate clauses introduced by words like weil, dass, wenn:

• ..., weil das Seminar voll ist.
• ..., dass die Zuhörer viele Fragen stellen.

So after aber and und in your sentence, we still have main clauses, so the verb stays in second position.