Instruktor vede začátečníky po sále.

Because it is the direct object of vede.

The verb vést means to lead / guide, and the person being led takes the accusative case.
The dictionary form is začátečník (beginner), but in the accusative plural it becomes začátečníky.

A useful comparison:

• začátečníci = nominative plural, beginners as the subject
• začátečníky = accusative plural, beginners as the object

So:

• Začátečníci vedou... = The beginners lead...
• Instruktor vede začátečníky... = The instructor leads the beginners...

Vede is the 3rd person singular present form of vést.

So it matches the singular subject instruktor:

• já vedu = I lead
• ty vedeš = you lead
• on / ona vede = he / she leads

In context, Czech present tense can often correspond to English:

• leads
• is leading

So vede can describe either a general action or something happening now, depending on context.

Because instruktor is the subject of the sentence, so it stays in the nominative case.

Its form here is the basic dictionary form:

• instruktor = nominative singular

Since it is doing the action of leading, it remains nominative.

Because the preposition po requires a different case here.

In this sentence, po takes the locative case, so sál changes to sále:

• sál = hall, gym, room
• po sále = around the hall / around in the hall

So sále is the locative singular form of sál.

Here po sále suggests movement around within the hall.

It does not just mean being located there. It implies moving through the space, for example while showing people where to go or guiding them around.

A useful contrast:

• v sále = in the hall (location)
• po sále = around the hall / around in the hall (movement within it)

So the sentence is not just saying where they are, but also how the movement happens.

Because Czech does not have articles like English.

So Czech simply says:

• instruktor
• začátečníky
• sále

and the context tells you whether English should use the, a, or no article at all.

That is very normal in Czech. Learners often want to add an article mentally, but Czech just does not need one.

It can mean either, depending on context.

Czech present tense often covers both:

• he leads
• he is leading

So Instruktor vede začátečníky po sále could describe:

• a general situation: The instructor leads beginners around the hall
• a current action: The instructor is leading the beginners around the hall

Only the wider context tells you which is meant.

Yes. Czech word order is much more flexible than English word order because the case endings show the grammatical roles.

This sentence has a neutral order:

• Instruktor vede začátečníky po sále.

But other orders are possible, for example:

• Po sále vede instruktor začátečníky.
• Začátečníky vede instruktor po sále.

The meaning stays broadly the same because:

• instruktor is still the subject
• začátečníky is still the object

What changes is mainly emphasis or information focus.

Grammatically, začátečník is a masculine animate noun.

That means:

• for a group of men, začátečníky is normal
• for a mixed group, Czech also normally uses the masculine animate plural
• for a group of women only, you would usually use začátečnice

So this form does not necessarily mean the group is all male. It may also refer to a mixed group.

Vést is imperfective.

That fits well here, because the sentence describes the action as an ongoing activity or general process of guiding people around.

Czech often uses different prefixed verbs for more specific perfective meanings, such as:

• dovést = lead someone to a destination
• odvést = lead someone away
• přivést = bring / lead someone to a place
• provést = guide someone through something

So plain vést is the natural choice when the focus is simply on the act of leading.

Not always.

Sál can mean a hall, large room, gym space, or similar kind of open indoor area, depending on context.

So po sále might be translated in different ways in natural English, for example:

• around the hall
• around the room
• around the gym

The exact English word depends on what kind of space is meant.