Mam potwierdzenie nadania.

Because mam is the 1st person singular of mieć, meaning to have.
So mam = I have.

In Polish, possession is usually expressed with mieć, just like in English:

• Mam bilet. = I have a ticket.
• Mam potwierdzenie nadania. = I have proof/confirmation of posting.

Jestem means I am, so it would not fit here.

Polish often leaves out subject pronouns because the verb ending already shows who the subject is.

• mam already means I have
• masz means you have
• ma means he/she/it has

So Mam potwierdzenie nadania is completely natural.
You could say Ja mam potwierdzenie nadania, but ja adds emphasis, like:

• Ja mam potwierdzenie, a ty nie. = I have the confirmation, and you don’t.

Potwierdzenie is the direct object of mam, so it is in the accusative case.

However, potwierdzenie is a neuter noun, and for many neuter nouns the nominative and accusative singular look the same. So:

• nominative: potwierdzenie
• accusative: potwierdzenie

That is why the word does not visibly change.

Because nadania is the genitive singular form of nadanie.

This structure is very common in Polish:

• potwierdzenie czego? = confirmation of what?
• potwierdzenie nadania = confirmation of posting / dispatch

So the second noun goes into the genitive after potwierdzenie.

A similar pattern:

• potwierdzenie odbioru = confirmation of receipt
• data wysłania = date of sending
• numer przesyłki = parcel number

In this context, nadanie means posting, dispatch, or sending off, especially through the post or a courier.

It is commonly used when you hand over a letter or parcel to be sent.

So potwierdzenie nadania usually means something like:

• proof of posting
• posting confirmation
• receipt confirming dispatch

It is especially common in postal and official contexts.

Usually, yes. Most often it refers to a document or receipt showing that a letter or parcel was sent.

For example, after mailing something at the post office, you may receive:

• potwierdzenie nadania
• dowód nadania

In broader contexts, Polish might use different words depending on what was sent:

• potwierdzenie wysłania e-maila = confirmation that an email was sent
• potwierdzenie złożenia wniosku = confirmation of submitting an application

So nadanie strongly suggests postal/courier dispatch.

They are very close in meaning and are often interchangeable in postal situations.

A rough distinction:

• potwierdzenie nadania = confirmation of posting/dispatch
• dowód nadania = proof of posting

In practice, both can refer to the receipt or document showing that something was sent.
You will hear both, especially at the post office.

Yes. Polish word order is more flexible than English because grammatical relationships are shown by endings, not only by position.

The neutral, most natural order here is:

• Mam potwierdzenie nadania.

But other orders are possible for emphasis, for example:

• Potwierdzenie nadania mam. = emphasizes that it is the confirmation that I have
• Ja mam potwierdzenie nadania. = emphasizes I

Even though other orders are possible, the original version is the best default choice for learners.

Yes, but the nuance is a bit different.

• nadanie is especially common for posting/dispatching a physical item through post or courier
• wysłanie is broader and simply means sending

So:

• potwierdzenie nadania sounds very natural for a letter or parcel
• potwierdzenie wysłania could work in other situations too, such as messages, emails, files, or more general sending

In a post-office context, potwierdzenie nadania is the more standard phrase.

A rough guide:

• mam → like mahm
• potwierdzenie → roughly pot-vyer-DZE-nye
• nadania → roughly na-DA-nya

Stress in Polish usually falls on the second-to-last syllable of a word:

• potwierDZEnie
• naDAnia

A few sound notes:

• w sounds like English v
• dz is like the sound in beds
• ie and ia often create a soft y/ya quality in pronunciation

So the whole sentence sounds roughly like:

mahm pot-vyer-DZE-nye na-DA-nya