Learn Hardcore Croatian: Učitelj drži govor u dvorani. - The teacher is giving a speech in the hall.

držati govor – ongoing or habitual action:
- Učitelj drži govor u dvorani. = The teacher is giving a speech / gives a speech in the hall.
There is also a perfective form održati govor (to give/complete a speech), used when you focus on the fact that the speech is (or will be) completed:
- Učitelj će održati govor. = The teacher will give a speech (and finish it).

What case is govor in here, and why does it look like the basic form?

Govor is in the accusative singular case, because it is the direct object of the verb drži (učitelj is holding what? → govor).

For masculine inanimate nouns like govor:

Nominative singular (dictionary form): govor
Accusative singular: govor (same form as nominative)

So it looks like the basic form, but in this sentence it functions grammatically as accusative.

Why is it u dvorani and not u dvorana or u dvoranu?

The preposition u can take either locative or accusative, depending on meaning:

u + locative = location (where?)
- Učitelj drži govor u dvorani.
  The teacher is giving a speech in the hall. (static location → locative)
u + accusative = direction (into where?)
- Učitelj ulazi u dvoranu.
  The teacher is entering the hall. (movement into → accusative)

Here we are talking about where the speech is taking place (no movement), so we use locative singular:

Nominative: dvorana (hall)
Locative: (u) dvorani

That is why it is u dvorani.

What gender and case is učitelj, and what would the feminine form be?

In Učitelj drži govor u dvorani:

učitelj is masculine, singular, nominative (the subject of the sentence).

Basic forms:

masculine: učitelj = teacher (male or generic)
feminine: učiteljica = female teacher

Examples:

Učitelj drži govor u dvorani. – The (male) teacher is giving a speech in the hall.
Učiteljica drži govor u dvorani. – The (female) teacher is giving a speech in the hall.

Could you use profesor or nastavnik instead of učitelj? Are they the same?

You can replace učitelj with other words, but they are not completely identical:

učitelj – usually primary (elementary) school teacher, sometimes generic teacher
nastavnik – teacher in higher grades (middle / high school), focus on subject teaching
profesor – more formal; high-school teacher or university professor

All would be grammatically correct in this sentence:

Profesor drži govor u dvorani.
Nastavnik drži govor u dvorani.
Učitelj drži govor u dvorani.

The choice mainly changes the type/status of the teacher, not the grammar.

Does the Croatian present tense here mean is giving or gives? How do I choose?

The Croatian present tense (drži) covers both English:

present simple (gives a speech)
present continuous (is giving a speech)

Učitelj drži govor u dvorani. can mean:

The teacher is giving a speech in the hall (right now).
The teacher gives a speech in the hall (as a regular activity / official program).

The exact nuance comes from context, not from verb form. Croatian does not have a separate continuous tense like English does.

What is the difference between držati govor and održati govor?

They form an aspect pair (imperfective vs perfective):

držati govor (imperfective) – focuses on the process or repetition:
- Učitelj drži govor u dvorani.
  The teacher is giving a speech in the hall.
održati govor (perfective) – focuses on the completed action:
- Učitelj je održao govor u dvorani.
  The teacher gave (and finished) a speech in the hall.
- Učitelj će održati govor sutra.
  The teacher will give a speech tomorrow.

So držati = in progress / habitual; održati = one whole, completed event.

Can the word order change, and if so, what difference does it make?

Yes, Croatian word order is flexible. The neutral order here is:

Učitelj drži govor u dvorani.
Subject – Verb – Object – Place

Possible variants (all grammatical, but with different emphasis or rhythm):

U dvorani učitelj drži govor.
Emphasizes the place first: In the hall, the teacher is giving a speech.
Govor drži učitelj u dvorani.
Emphasizes govor (the speech), maybe contrasting who is giving it or what is happening.
Učitelj u dvorani drži govor.
Slight focus on in the hall (as opposed to some other place).

Meaning stays basically the same, but the focus shifts depending on what comes first.

How would the sentence change in the plural (more teachers, more speeches, more halls)?

Some useful plurals:

More teachers, one speech, one hall
- Učitelji drže govor u dvorani.
  The teachers are giving a speech in the hall.
- učitelji = nominative plural of učitelj
- drže = 3rd person plural of držati
One teacher, more speeches, one hall
- Učitelj drži govore u dvorani.
  The teacher is giving speeches in the hall.
- govore = accusative plural of govor
One teacher, one speech, more halls (more general statement)
- Učitelj drži govor u dvoranama.
  The teacher gives a speech in halls. / …in various halls.
- dvoranama = locative plural of dvorana

The verb must agree in number with the subject (učitelj / učitelji).

What exactly does dvorana mean? Is it the same as room?

Dvorana usually means a large hall, not just any room. Contexts:

sports hall (gym)
concert hall
large lecture hall
ceremonial hall

For a normal room, Croatians usually say:

soba – room (general, in a house or flat)
učionica – classroom
sala – hall/large room (often used especially for events, weddings, conferences)

So u dvorani suggests a bigger, more formal space than a simple room.

How do you conjugate držati in the present tense?

Present tense of držati (to hold):

ja držim – I hold / I am holding
ti držiš – you hold (singular, informal)
on / ona / ono drži – he / she / it holds
mi držimo – we hold
vi držite – you hold (plural or formal)
oni / one / ona drže – they hold

In the sentence:

Učitelj drži govor… → 3rd person singular: drži.

How should I pronounce učitelj and drži, especially č and ž?

Approximate pronunciation:

učitelj → [OO-chee-telʲ]
- u = like oo in boot
- č = like ch in church
- i = like ee in see
- lj is a palatal l, similar to lli in million (in many accents)
drži → [DR-zhih]
- r = rolled/flapped (like Spanish r in pero)
- ž = like s in measure or zh in vision
- i = like ee in see (but short)

Stress is usually on the first syllable: Ū-čitelj, DR-ži (stress patterns can vary by dialect, but this is a good guideline).

Why is there no the or a in front of učitelj or govor? How do you know if it means the teacher or a teacher?

Croatian has no articles (no direct equivalents of a/an or the). Nouns appear without them:

učitelj = teacher (could be a teacher or the teacher)
govor = speech (could be a speech or the speech)

Whether you translate it as a or the in English depends on context:

If both speaker and listener know which teacher: the teacher
If you are introducing this teacher for the first time: a teacher

So:

Učitelj drži govor u dvorani.
could be translated as either
A teacher is giving a speech in the hall
or
The teacher is giving a speech in the hall,
depending on the surrounding context.