Proszę pani, czy mogłaby pani dodać kawałek cytryny do herbaty?

Here Proszę pani is a polite way to get a woman’s attention, similar to Excuse me, ma’am or Ma’am.

Literally, proszę is related to please, but in this expression the whole phrase works as a set formula of address. It is very common when speaking politely to a woman you do not know well, especially in service situations.

No. You can say:

Czy mogłaby pani dodać kawałek cytryny do herbaty?

and it is still perfectly polite.

Adding Proszę pani makes it sound more like you are first getting the woman’s attention before making the request.

The two pani do different jobs.

• The first one is part of Proszę pani, the address formula.
• The second one is the polite you in the request: czy mogłaby pani dodać...

In Polish, formal you is expressed with pan or pani, and the verb is used in the third person form. So mogłaby pani literally looks a bit like could madam, but it means could you in a formal way.

That is simply how the formal system works in modern Polish. Instead of using a separate pronoun like English you, Polish often uses pan for a man and pani for a woman.

So:

• Czy może pani...? = Can you...? said formally to a woman
• Czy mógłby pan...? = Could you...? said formally to a man

The verb behaves grammatically like third person, even though the meaning is second person.

Mogłaby pani uses the conditional and sounds softer and more polite than może pani.

Compare:

• Czy może pani dodać...? = Can you add...?
• Czy mogłaby pani dodać...? = Could you add...?

The second version is less direct and therefore more polite. In requests, Polish often uses the conditional this way, just like English uses could instead of can.

Because the sentence is addressed to a woman.

In the conditional/past-type forms, Polish shows gender:

• mógłby pan — to a man
• mogłaby pani — to a woman

So the ending tells you the gender of the person you are speaking to in this formal pattern.

Czy introduces a yes/no question.

So:

• Mogłaby pani dodać...? can be a question in speech, especially with intonation
• Czy mogłaby pani dodać...? is a very clear, standard yes/no question

In English, we change word order to make a question. In Polish, czy is one common way to mark that the sentence is a question.

Because it depends on mogłaby.

After móc (can / be able to / could), Polish usually uses an infinitive:

• mogę dodać — I can add
• może pani dodać — you can add
• mogłaby pani dodać — could you add

So dodać is there because mogłaby is the finite verb, and dodać gives the main action.

Dodać is perfective, and dodawać is imperfective.

Here the speaker is asking for one complete action: add one piece of lemon to the tea. For a single finished act, perfective dodać is the natural choice.

Very roughly:

• dodać = add it once / complete the action
• dodawać = be adding / add repeatedly / add in a general sense

Kawałek means piece. In Polish, nouns like piece, glass, cup, slice, and so on are often followed by a noun in the genitive:

• kawałek chleba — a piece of bread
• szklanka wody — a glass of water
• plasterek cytryny — a slice of lemon

So cytryny is genitive singular and means of lemon.

Also, kawałek here is the direct object of dodać. Since kawałek is masculine inanimate, its accusative form is the same as the nominative: kawałek.

Because the verb pattern is dodać coś do czegoś — to add something to something.

The preposition do takes the genitive, so:

• herbata → nominative
• herbaty → genitive after do

So do herbaty means to the tea.

It is understandable, but in this context many speakers would more naturally say plasterek cytryny, because lemon for tea is usually thought of as a slice, not just a general piece.

So these are both possible, but:

• kawałek cytryny = a piece of lemon
• plasterek cytryny = a slice of lemon

For tea, plasterek cytryny is often the more idiomatic choice.

Yes. Polish word order is more flexible than English word order.

For example, these are all possible:

• Czy mogłaby pani dodać kawałek cytryny do herbaty?
• Czy pani mogłaby dodać kawałek cytryny do herbaty?
• Mogłaby pani dodać kawałek cytryny do herbaty?

The version you have is very natural and standard. Changing the order can slightly change emphasis, but not the basic meaning.

It is quite polite and appropriate for speaking to a woman you do not know well, especially in a restaurant, café, hotel, or similar setting.

It would sound too formal with a close friend. In an informal situation with a woman you know well, you might say:

• Czy mogłabyś dodać kawałek cytryny do herbaty?
• Dodasz kawałek cytryny do herbaty?

So mogłaby pani is the formal, respectful version.