Pierwszą opłatę trzeba zapłacić jeszcze przed końcem tygodnia.

Because pierwszą opłatę is the direct object of zapłacić (to pay), so it takes the accusative case.

• pierwsza opłata = nominative, the basic dictionary-like form
• pierwszą opłatę = accusative, used here because it is the thing being paid

This is very common in Polish:

• Mam książkę = I have a book
• Czytam gazetę = I am reading a newspaper
• Zapłacić opłatę = to pay a fee

Since opłata is a feminine noun, both the adjective and the noun change:

• pierwsza opłata → nominative
• pierwszą opłatę → accusative

Trzeba means something like it is necessary, one must, or it has to be done.

In this sentence, trzeba zapłacić means:

• it is necessary to pay
• one has to pay
• it must be paid

This is a very common Polish impersonal structure:

• Trzeba iść = One has to go
• Trzeba czekać = One has to wait
• Trzeba zapłacić = One has to pay

There is no specific subject like I, you, or they. Polish often uses trzeba + infinitive when speaking generally or impersonally.

Because zapłacić is the perfective form, while płacić is imperfective.

• płacić = to be paying, to pay in a general/repeated/ongoing sense
• zapłacić = to pay, with focus on completing the action

Here the sentence is about a single completed payment that must happen before a deadline, so zapłacić fits better.

Compare:

• Trzeba płacić regularnie. = You have to pay regularly.
• Trzeba zapłacić do piątku. = You have to pay by Friday.

So in your sentence, the idea is not just be paying, but make sure the payment gets completed.

Here jeszcze means still, yet, or as early as / already before it is too late, depending on context.

In jeszcze przed końcem tygodnia, it adds the idea of:

• before the end of the week is reached
• while there is still time
• already before the week ends

It often gives a sense of urgency or remaining time.

Examples:

• Jeszcze dziś = still today / as early as today
• Jeszcze przed obiadem = before lunch
• Musisz to zrobić jeszcze dziś. = You must do it today, before the day ends

So here it suggests: the payment must be made before the week is over, while there is still time.

Because przed (before) takes the instrumental case when used in this time meaning.

So:

• koniec = end
• końcem = instrumental singular

That is why you get:

• przed końcem = before the end

This is the normal pattern:

• przed obiadem = before lunch
• przed spotkaniem = before the meeting
• przed końcem tygodnia = before the end of the week

Because koniec often takes a noun in the genitive, just like end of... in English.

So:

• koniec tygodnia = end of the week
• koniec miesiąca = end of the month
• koniec roku = end of the year

In your sentence, the phrase is built like this:

• przed
  • końcem (instrumental)
• tygodnia (genitive, because it depends on koniec)

So literally it is:

• before [the] end [of the] week

It can often be understood as either, depending on context.

Opłata usually means:

• fee
• charge
• payment due

So pierwsza opłata can mean:

• the first fee in a series
• the first installment/payment
• the initial charge

In many real-life situations, English could translate it naturally as the first payment even though the Polish noun is opłata.

Not an explicit one. The sentence is impersonal.

Polish often leaves out a specific subject when the meaning is general:

• Trzeba pracować. = One has to work.
• Nie wolno palić. = Smoking is not allowed.
• Można wejść. = One may enter / You can come in.

So Pierwszą opłatę trzeba zapłacić... does not say exactly who must pay. The context tells you that.

In English, we often use:

• you have to
• one has to
• it has to be paid

depending on style and situation.

Yes, Polish word order is fairly flexible, although different orders change the emphasis.

Your sentence:

• Pierwszą opłatę trzeba zapłacić jeszcze przed końcem tygodnia.

This sounds natural and puts early focus on the first payment/fee.

Other possible orders include:

• Trzeba zapłacić pierwszą opłatę jeszcze przed końcem tygodnia.
• Jeszcze przed końcem tygodnia trzeba zapłacić pierwszą opłatę.

These all mean roughly the same thing, but the emphasis shifts:

• starting with Pierwszą opłatę highlights what must be paid
• starting with Jeszcze przed końcem tygodnia highlights the deadline
• starting with Trzeba zapłacić highlights the obligation

You could understand it that way, but it would sound unnatural in English.

A more natural English translation would be:

• The first payment must be made before the end of the week.
• The first fee must be paid before the end of the week.
• The first payment has to be made before the end of the week.

The word jeszcze is often not translated word-for-word as still in English. Instead, its nuance is absorbed into the overall meaning of the deadline.

Yes, it is normal.

In Polish, zapłacić opłatę is a standard collocation and means to pay a fee/charge.

Examples:

• zapłacić rachunek = pay a bill
• zapłacić karę = pay a fine
• zapłacić opłatę = pay a fee

Depending on context, English may prefer:

• pay the fee
• make the payment
• pay the charge

So the Polish is perfectly natural even if English might choose slightly different wording.