Platební výměr leží před správcem poplatku.

Because it is the subject of the sentence: it is the thing that lies somewhere.

• platební výměr = the subject
• leží = the verb
• před správcem poplatku = the location phrase

So Czech uses the nominative for platební výměr, just as English uses the basic subject form.

Because the preposition před takes the instrumental case when it describes a location.

Here, před správcem poplatku means in front of the fee/tax administrator, so správce must be in the instrumental singular:

• nominative: správce
• instrumental: správcem

This is one of the most common things learners need to remember with Czech prepositions: the preposition often determines the case.

Because it depends on správce.

správce poplatku means literally administrator of the fee/charge. In Czech, nouns like správce often take another noun in the genitive to show whose / of what.

So:

• správce = administrator
• poplatku = of the fee / charge

This is similar to English the administrator of the fee, except Czech usually prefers the genitive instead of using a separate word like of.

Před can take two different cases, depending on meaning:

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

In your sentence, it is location, so Czech uses the instrumental:

• Platební výměr leží před správcem poplatku.

If it were about movement, you would expect the accusative instead.

So the key idea is:

• where? → instrumental
• to where? → accusative

Leží is from ležet, which means to lie or to be lying.

It suggests that the document is in a horizontal resting position, probably on a desk, table, or similar surface. That makes it more vivid and physical than just je (is).

Compare:

• Platební výměr je před správcem poplatku.
  = The document is in front of the administrator.
  This is more neutral.

• Platební výměr leží před správcem poplatku.
  = The document is lying in front of the administrator.
  This suggests actual physical placement.

For papers, books, and objects on a surface, ležet is very natural.

Yes, adjectives do agree with nouns in Czech.
Here, platební agrees with výměr in gender, number, and case.

The reason it may look surprising is that platební is a soft adjective of the -í type, and these forms often stay the same across several categories.

In this sentence:

• výměr is masculine singular nominative
• so the adjective is also masculine singular nominative
• the correct form is platební

So the adjective is agreeing; it just happens that the visible form is platební.

Yes, it is largely an official administrative/legal term rather than an everyday casual phrase.

That matters because learners sometimes try to understand it word by word, but in practice it functions as a set phrase in formal Czech. So it is better to learn it as one unit.

This kind of thing is very common in bureaucratic Czech:

• formal noun + formal adjective
• often used in tax, legal, or administrative contexts

So even if you can analyze the grammar, it is useful to remember that it behaves like a standard official expression.

No, Czech word order is fairly flexible.

The sentence as given:

• Platební výměr leží před správcem poplatku.

is a normal, straightforward order.

But Czech could also say:

• Před správcem poplatku leží platební výměr.

That version puts more attention on the location first.

In general:

• earlier in the sentence = often known information or emphasis
• later in the sentence = often newer or more important information

So word order in Czech is not random, but it is less rigid than in English.

Because Czech has no articles like English a/an and the.

Czech usually leaves definiteness to be understood from:

• context
• word order
• situation
• common sense

So Platební výměr can mean something like:

• a payment assessment
• the payment assessment

depending on context.

English speakers often want to know exactly where the went, but in Czech there is simply no separate article word to add.

You usually learn a Czech noun together with its gender, because gender affects adjective agreement, verb forms in the past, and declension.

Here, výměr is masculine inanimate.

You can see the grammar working with it:

• platební výměr → adjective agrees with a masculine noun
• leží → singular verb, because the subject is singular

For practical learning, it is best to memorize:

• ten výměr
  not just výměr

Using the article-like demonstrative ten while learning can help you remember the gender.

Yes:

• Platební — adjective, modifying výměr
• výměr — masculine inanimate singular nominative, the subject
• leží — 3rd person singular present of ležet
• před — preposition
• správcem — masculine animate singular instrumental of správce
• poplatku — masculine inanimate singular genitive of poplatek

So the structure is:

• [Subject] + [Verb] + [Prepositional phrase]

More literally:

• The payment assessment lies in front of the administrator of the fee.

That grammatical skeleton is the main thing to notice.