Kobieta przy okienku powiedziała, że mogę wpłacić tę kwotę dopiero jutro rano.

Because kobieta is feminine, the past-tense verb has to agree with it.

• kobieta = woman
• powiedziała = said for a feminine subject
• powiedział would be used for a masculine subject

So the structure is:

• Kobieta ... powiedziała = The woman ... said

After the preposition przy when it means by / at / next to, Polish uses the locative case.

So:

• okienko = little window / service window
• przy okienku = at the window / at the counter window

The locative form of okienko is okienku.

This is a very common pattern:

• przy stole = at the table
• przy drzwiach = by the door
• przy okienku = at the window

In this sentence, okienko usually means a service counter window, like in a bank, post office, or office.

Okienko is a diminutive form of okno, but in many situations it is the normal word for a service window or small counter window.

So here it does not necessarily sound cute. It is just the usual word in this context.

Compare:

• okno = window
• okienko = small window / counter window / service window

In places like banks or ticket offices, przy okienku is extremely natural.

Because mogę is present tense, and Polish often keeps the tense that matches the real situation rather than shifting it back the way English often does.

English often does this:

• She said that I could pay...

But in Polish, if the permission or possibility is still valid now and concerns the future action, mogę is very natural:

• powiedziała, że mogę wpłacić... = she said that I can pay in...

Polish does not have the same strict backshifting rule as English.

Also, mogę does not show the speaker’s gender.
If you used a past form like mogłem or mogłam, then it would show gender.

Here it most naturally means I am allowed to or I can in the sense of permission/possibility.

So the idea is:

• the woman told me that it is only possible / permitted for me to deposit the money tomorrow morning

With móc, English translations can vary:

• can
• may
• be able to
• be allowed to

In this sentence, am allowed to / can both work well.

Wpłacić is the perfective form, and it refers to completing a single action: making the deposit.

• wpłacić = to pay in / deposit once, successfully, as a completed act
• wpłacać = to be paying in / to pay in repeatedly / habitually / in an ongoing way

In this sentence, the speaker is talking about one specific future deposit, so perfective wpłacić is the natural choice.

Compare:

• Mogę wpłacić tę kwotę jutro. = I can deposit this amount tomorrow.
• Codziennie wpłacam pieniądze. = I deposit money every day.

Tę kwotę is in the accusative case because it is the direct object of wpłacić.

Base forms:

• ta = this
• kwota = amount

Accusative forms:

• tę
• kwotę

So:

• wpłacić tę kwotę = to deposit this amount

This is a common feminine singular accusative pattern:

• ta książka → tę książkę
• ta kawę is wrong; correct is tę kawę
• ta kwota → tę kwotę

You may also hear tą kwotę in everyday speech, but in standard grammar tę kwotę is the expected form here.

Here dopiero means only, not until, or no earlier than.

So:

• dopiero jutro rano = only tomorrow morning / not until tomorrow morning

It emphasizes delay or lateness from the speaker’s point of view.

Compare:

• Mogę to zrobić dopiero jutro. = I can only do it tomorrow.
• Przyszedł dopiero o dziesiątej. = He only arrived at ten / as late as ten.

So in your sentence, dopiero tells us that today is too early; tomorrow morning is the earliest possible time.

Jutro rano is the normal, natural order for tomorrow morning in Polish.

• jutro = tomorrow
• rano = in the morning / morning-time

Together:

• jutro rano = tomorrow morning

Polish word order is flexible, but some combinations are much more idiomatic than others. Rano jutro would sound unusual in most contexts.

Similar expressions:

• dzisiaj rano = this morning
• wczoraj rano = yesterday morning
• jutro wieczorem = tomorrow evening

Że means that and introduces a subordinate clause.

So:

• powiedziała, że... = she said that...

This is one of the most common ways to report speech or thoughts in Polish.

Examples:

• Wiem, że... = I know that...
• Myślę, że... = I think that...
• Powiedział, że... = He said that...

In English, that is often omitted. In Polish, że is very commonly stated.

It breaks down like this:

• Kobieta przy okienku = the woman at the counter window
• powiedziała = said
• że = that
• mogę = I can / I’m allowed to
• wpłacić tę kwotę = deposit this amount
• dopiero jutro rano = only tomorrow morning / not until tomorrow morning

So the sentence has:

1. a main clause: Kobieta przy okienku powiedziała
2. a subordinate clause: że mogę wpłacić tę kwotę dopiero jutro rano

No, it does not.

The form mogę is first person singular present tense, and it does not show gender.

So both a man and a woman could say:

• mogę wpłacić tę kwotę...

If the sentence used a past-tense first-person form, then gender would appear:

• mogłem = I could / I was able to / I was allowed to, masculine
• mogłam = I could / I was able to / I was allowed to, feminine

But in your sentence, the speaker’s gender is unknown.

Yes, Polish word order is flexible, but different orders can sound more or less natural or shift emphasis.

The given version is very natural:

• Kobieta przy okienku powiedziała, że mogę wpłacić tę kwotę dopiero jutro rano.

You could also hear variations like:

• Kobieta przy okienku powiedziała, że tę kwotę mogę wpłacić dopiero jutro rano.
• Powiedziała kobieta przy okienku, że mogę wpłacić tę kwotę dopiero jutro rano.
  This is less neutral and gives a different emphasis or style.

In neutral everyday Polish, the original wording is a very good standard version.

Yes. Wpłacić usually means to pay in, deposit, or pay into an account/fund.

It is commonly used for money paid:

• into a bank account
• at a cashier’s desk
• toward a fee or bill
• as an installment or contribution

So wpłacić tę kwotę strongly suggests a financial payment/deposit, not just any kind of paying.

That is why wpłacić fits well with kwota.