Płacę pięćdziesiąt złotych.

Because Polish often drops subject pronouns when the verb already makes the subject clear.

Płacę means I pay / I’m paying, and the ending -ę tells you it is 1st person singular.

So:

• Płacę pięćdziesiąt złotych. = I’m paying fifty zlotys.
• Ja płacę pięćdziesiąt złotych. = also correct, but ja adds emphasis, like I am the one paying.

Płacę is the 1st person singular present-tense form of the verb płacić.

So the pattern is:

• ja płacę = I pay / I’m paying
• ty płacisz = you pay
• on/ona płaci = he/she pays

Because płacić is imperfective, płacę can mean either:

• I pay (habitually), or
• I’m paying (right now)

The exact meaning depends on context.

A few important pronunciation points:

• ł sounds like English w
• ę is a nasal vowel; at the end of a word it is often pronounced only lightly nasally in normal speech
• ć is a soft sound, somewhat like a softened ch/tch
• zł at the start of złotych can feel tricky at first; say the z and then quickly go into w

Stress in Polish usually falls on the second-to-last syllable, so here you get:

• PŁA-cę
• pięć-DZIE-siąt
• ZŁO-tych

A learner-friendly approximation would be something like:

PWA-tse pyeń-JE-shont ZWO-tikh

Not perfect, but close enough to help at first.

Because after 5 and higher numbers, Polish normally uses the noun in the genitive plural.

So:

• 1 złoty
• 2 złote
• 3 złote
• 4 złote
• 5 złotych
• 10 złotych
• 50 złotych

That is why pięćdziesiąt złotych is correct.

This is a very useful pattern to memorize:

• 1 złoty
• 2, 3, 4 złote
• 5+ złotych

Examples:

• jeden złoty
• dwa złote
• cztery złote
• pięć złotych
• pięćdziesiąt złotych

Also note the teen numbers:

• 12 złotych
• 14 złotych

And numbers ending in 2, 3, 4 usually go back to złote, unless they are in the teens:

• 22 złote
• 23 złote
• 24 złote
• but 12 złotych, 13 złotych, 14 złotych

Yes — at least in the form of the noun.

In pięćdziesiąt złotych, the noun złotych is in the genitive plural, because that is the normal pattern after numerals 5 and above.

This can feel strange to English speakers, because there is no of in English here. But in Polish, after higher numbers, the noun often appears in a genitive form:

• pięć książek = five books
• dziesięć dolarów = ten dollars
• pięćdziesiąt złotych = fifty zlotys

So yes, the form is genitive, even though the whole phrase is simply the amount being paid.

Yes — that is very common and natural in writing.

• Płacę pięćdziesiąt złotych.
• Płacę 50 zł.

Both are fine. The second one is just shorter and more practical.

In speech, 50 zł would normally be read as pięćdziesiąt złotych.

This is mainly a question of aspect.

• płacę = I pay / I’m paying
  (imperfective: ongoing, repeated, or uncompleted action)
• zapłacę = I will pay / I’ll pay
  (perfective: a completed payment in the future)

Examples:

• Płacę teraz. = I’m paying now.
• Zaraz zapłacę. = I’ll pay in a moment.

So in your sentence, płacę pięćdziesiąt złotych sounds like I’m paying fifty zlotys or I pay fifty zlotys, depending on context.

Yes. Polish word order is more flexible than English because the endings carry a lot of grammatical information.

The most neutral version is:

• Płacę pięćdziesiąt złotych.

But you could also hear:

• Ja płacę pięćdziesiąt złotych. — emphasis on I
• Pięćdziesiąt złotych płacę. — emphasis on the amount, but less neutral

So the standard sentence is the best one to learn first, but other orders are possible for emphasis or style.

You usually add za + accusative.

For example:

• Płacę pięćdziesiąt złotych za bilet. = I’m paying fifty zlotys for the ticket.
• Płacę sto złotych za hotel. = I’m paying one hundred zlotys for the hotel.

So if you want to mention the thing being paid for, za is very often the word you need.

Yes. In standard Polish, 50 is written as the single word pięćdziesiąt.

This is normal for many Polish numerals:

• jedenaście = 11
• dwadzieścia = 20
• pięćdziesiąt = 50

So pięćdziesiąt złotych is the normal written form, not something split into separate words.