Správce poplatku může vyměřit trojnásobek.

Because správce poplatku literally means administrator/collector of the fee. In Czech, a noun like správce often takes another noun in the genitive to show what is being administered or managed:

• správce domu = manager of a building
• správce sítě = network administrator
• správce poplatku = fee administrator / fee collector

So:

• správce = nominative singular, the subject
• poplatku = genitive singular of poplatek

In this kind of sentence, it is often a legal or administrative term, so it may refer to the authority responsible for the fee, not just one individual person.

Even though správce is grammatically a singular masculine noun, in official language it can mean:

• a specific official
• an office
• the authority acting in that role

So the grammar is singular, but the real-world reference may be broader than one man.

It can correspond to both, but in this sentence may is often the better English match.

• can = ability
• may = permission or legal authority

In legal/official Czech, může often expresses that someone is allowed or authorized to do something. So here it is closer to:

• is allowed to
• has the right to
• may

Grammatically, může is the 3rd person singular present form of moci.

Because Czech modal verbs like moci work the same basic way as English modal verbs: the modal is the finite verb, and the main action appears as an infinitive.

So:

• může = may/can
• vyměřit = to assess / to impose / to levy

Together:

• může vyměřit = may assess / may impose

This is very normal Czech structure.

This is a question of aspect.

• vyměřit = perfective
• vyměřovat = imperfective

The perfective vyměřit presents the action as a single completed act: the authority assesses or imposes the amount.

That fits well here, because the sentence is about the possibility of carrying out that act.

If you used vyměřovat, it would sound more like:

• doing it repeatedly
• doing it as an ongoing process
• speaking about the activity in general

So může vyměřit is the natural choice for may assess/impose in a legal statement.

Trojnásobek is a noun, not an adjective or adverb. It means triple, three times the amount, or a threefold amount.

In this sentence it is the direct object of vyměřit, so it is in the accusative. But because it is an inanimate masculine noun, its accusative form is the same as the nominative:

• nominative: trojnásobek
• accusative: trojnásobek

So the structure is:

• Správce poplatku = subject
• může vyměřit = may assess/impose
• trojnásobek = direct object

Often, yes — at least logically.

Trojnásobek usually means three times something. In context, that something is often understood from the surrounding text, for example the fee amount itself.

So the sentence can feel like a shortened version of something like:

• může vyměřit trojnásobek poplatku
• může vyměřit trojnásobek této částky

But Czech often leaves that unstated if the context already makes it clear.

Not in the same way.

• trojnásobek = a noun: triple / three times the amount
• trojnásobně = an adverb: threefold / three times

In this sentence, the verb vyměřit needs an object, and trojnásobek supplies that object.

So:

• vyměřit trojnásobek = assess/impose triple the amount

Using trojnásobně would require a different structure and would not fit this sentence naturally.

It could change, because Czech word order is fairly flexible. The given order is neutral and natural for formal written language:

• Správce poplatku může vyměřit trojnásobek.

But other orders are possible for emphasis, for example:

• Trojnásobek může správce poplatku vyměřit.
  Emphasizes trojnásobek.

Changing the order does not automatically change the basic meaning, but it can change focus, emphasis, or style.

Not really. It sounds formal, administrative, and legal.

Two things especially give it that tone:

• správce poplatku as an official/legal term
• vyměřit in the sense of officially assessing or imposing an amount

So a learner should recognize this as official Czech, not casual conversation. It is the kind of sentence you might see in:

• regulations
• official notices
• legal texts
• municipal or tax documents