Nástupní místo je před výstupním místem.

Both are adjective + noun combinations:

• nástupní = boarding, for getting on
• výstupní = exit, for getting off
• místo = place, spot, location

So:

• nástupní místo = boarding place / boarding point
• výstupní místo = exit place / drop-off point / place for getting off

The adjectives come from the ideas of:

• nastoupit = to get on, board
• vystoupit = to get off, get out, disembark

So the sentence is built very literally.

Because the two nouns are in different cases.

• nástupní místo is the subject, so it is in the nominative
• výstupním místem comes after před, which here requires the instrumental

So:

• místo = nominative singular
• místem = instrumental singular

This is a very common Czech pattern: the form of the noun changes depending on its role in the sentence.

With před, Czech uses:

• instrumental for location: in front of / before
• accusative for movement toward a position in front of something

In this sentence, nothing is moving. It describes where something is:

• Nástupní místo je před výstupním místem. = The boarding point is in front of / before the exit point.

So před takes the instrumental.

Compare:

• Stojí před domem. = He is standing in front of the house.
• Postavil se před dům. = He moved to stand in front of the house.

That same location-vs-movement distinction is happening here.

Because the adjective has to agree with the noun it describes.

The noun místo is:

• neuter
• singular
• here in the instrumental

So the adjective must also be neuter singular instrumental:

• výstupní místo = nominative singular
• výstupním místem = instrumental singular

The adjective ending changes from -í to -ím, and the noun changes from -o to -em.

This is normal adjective agreement in Czech.

It is instrumental singular.

Breakdown:

• výstupním = instrumental singular of výstupní
• místem = instrumental singular of místo

So the whole phrase před výstupním místem means in front of the exit point.

Here it is most naturally spatial.

So the sentence means something like:

• The boarding point is in front of the exit point
• or The boarding point is before the exit point in a physical layout

Czech před can also be temporal:

• před obědem = before lunch
• před rokem = a year ago / before a year

But in this sentence, because both things are places, the spatial meaning is the normal one.

Because Czech has no articles.

So Czech does not have separate words corresponding directly to:

• a / an
• the

Whether something means a place, the place, or just place depends on context.

So:

• Nástupní místo can mean a boarding point or the boarding point
• výstupním místem can mean an exit point or the exit point

English has to choose; Czech usually does not.

Yes. Czech word order is more flexible than English.

You could also say:

• Před výstupním místem je nástupní místo.

This still means basically the same thing, but the emphasis changes:

• Nástupní místo je před výstupním místem.
  starts with the boarding point
• Před výstupním místem je nástupní místo.
  starts with the location

So the original sentence is neutral and clear, but other word orders are possible.

Yes. Je is the 3rd person singular form of být = to be.

So:

• je = is

In this sentence:

• Nástupní místo je před výstupním místem. = The boarding point is in front of the exit point.

Nothing unusual is happening with je here.

Usually, no—not in a neutral sentence like this.

Czech can sometimes omit a repeated noun if the context is very clear, but here that would sound incomplete or unnatural to most learners and in many contexts to native speakers as well.

So the full version is best:

• Nástupní místo je před výstupním místem.

Both phrases need their noun, because each adjective is describing its own place.

Místo is neuter.

That matters because adjectives must agree with the noun in:

• gender
• number
• case

So with místo, you get neuter forms such as:

• nástupní místo = nominative singular neuter
• výstupním místem = instrumental singular neuter

If the noun were masculine or feminine, the adjective endings would be different. So knowing that místo is neuter helps you predict the grammar around it.