Opłata zmienna jest wysoka.

Opłata is in the nominative singular.

That makes sense because it is the subject of the sentence — the thing being described as wysoka.

Its basic dictionary form is also opłata, so what you see here is the normal citation form:

• opłata = nominative singular
• opłaty = genitive singular or nominative plural, depending on context
• opłatę = accusative singular
• opłatą = instrumental singular

In this sentence, opłata is simply the subject: the fee / charge.

You are right that the usual neutral order is:

• zmienna opłata

So a learner may expect Zmienna opłata jest wysoka.

The version Opłata zmienna jest wysoka is still possible, but it sounds more:

• formal
• technical
• administrative
• sometimes slightly marked or specialized

Post-positioning the adjective can make the phrase feel more like a category label, as in official or business language.

So:

• zmienna opłata = the more everyday, neutral phrasing
• opłata zmienna = more formal/technical style

Because they both agree with opłata, which is:

• feminine
• singular
• nominative

In Polish, adjectives must agree with the noun they describe, and predicate adjectives also agree with the subject.

So:

• opłata = feminine singular nominative
• zmienna = feminine singular nominative
• wysoka = feminine singular nominative

Compare:

• wysoki koszt = a high cost (masculine)
• wysoka opłata = a high fee (feminine)
• wysokie wynagrodzenie = a high payment/remuneration (neuter)

Jest means is.

It is the 3rd person singular present tense of być = to be.

So the structure is:

• Opłata zmienna = the variable fee
• jest = is
• wysoka = high

English also needs is here, and so does standard Polish.

In standard Polish, no, not in a normal full sentence like this.

You should say:

• Opłata zmienna jest wysoka.

Not:

• Opłata zmienna wysoka.

Polish sometimes drops forms of to be in:

• headlines
• notes
• very informal fragments
• some special stylistic contexts

But for a normal declarative sentence, keep jest.

Yes — and for many learners, that is actually the more natural version to produce first.

Both are possible:

• Zmienna opłata jest wysoka.
• Opłata zmienna jest wysoka.

The difference is mostly one of style and emphasis, not basic meaning.

A good rule:

• use adjective + noun for the safest, most neutral word order
• recognize that noun + adjective may appear in formal, technical, or administrative language

Polish commonly uses wysoki / wysoka / wysokie with things like:

• fees
• prices
• rates
• taxes
• salaries
• costs

So wysoka opłata is the normal way to say a high fee.

Compare:

• wysoka cena = high price
• wysoki podatek = high tax
• wysokie koszty = high costs

Droga usually means expensive, and it is more often used for things, services, trips, etc. It is not impossible in some contexts, but wysoka opłata is the standard collocation.

Duża means big/large, so it is less precise here.

Grammatically, wysoka is the predicate adjective — it comes after jest and tells us a property of the subject.

So the structure is:

• subject: Opłata zmienna
• verb: jest
• predicate adjective: wysoka

Even though in English we might loosely say it describes the fee, in grammatical terms it is not just an adjective inside the noun phrase. It is part of the predicate: is high.

Because Polish has no articles.

English distinguishes:

• a fee
• the fee

Polish does not use separate words like a or the. Context tells you whether something is:

• indefinite
• definite
• generic

So Opłata zmienna jest wysoka could correspond to:

• The variable fee is high
• A variable fee is high
• Variable fee is high in a very context-dependent translation

In real usage, context usually makes the intended meaning clear.

A few useful points:

• opłata: the ł sounds like English w
  • roughly: o-PWA-ta
• zmienna: the zmi begins with a soft cluster; the nn is pronounced like a softened n
  • roughly: ZMYEN-na
• jest: roughly like yest, but with a shorter vowel
• wysoka: vy-SO-ka, because Polish w sounds like English v

Stress in Polish is usually on the second-to-last syllable:

• opłata
• zmienna
• wysoka

Here zmienna means variable in the sense of not fixed.

In business, billing, finance, or technical contexts, zmienny / zmienna / zmienne often contrasts with stały / stała / stałe:

• opłata zmienna = variable fee
• opłata stała = fixed fee

So in this sentence, zmienna is not just saying the fee changes in a vague everyday sense. It often suggests a specific category: a fee whose amount depends on some factor.

Not exactly.

These words overlap, but they are used differently:

• opłata = fee, charge, payment required for a service, permit, use, etc.
• cena = price
• koszt = cost

So:

• opłata is something you are charged
• cena is the listed price of something
• koszt is the cost, often from the buyer’s or producer’s perspective

In this sentence, opłata is the right kind of word for a fee or charge rather than a general price.