Ola jest moją narzeczoną, a ja jestem jej narzeczonym.

They are both forms of the verb być (to be), but they match different subjects:

• jest = he/she/it is
• jestem = I am

So in the sentence:

• Ola jest moją narzeczoną = Ola is my fiancée
• a ja jestem jej narzeczonym = and I am her fiancé

Polish verbs usually change depending on the person, much more like Spanish or French than like modern English.

Because after być in this kind of sentence, Polish very often uses the instrumental case for the noun phrase describing who someone is.

So:

• basic form (nominative): moja narzeczona
• instrumental form: moją narzeczoną

That is why you get:

• Ola jest moją narzeczoną

instead of Ola jest moja narzeczona.

In modern Polish, the instrumental after być is the normal choice in sentences like this.

Because the sentence refers to two different people of different genders:

• narzeczona = fiancée (female)
• narzeczony = fiancé (male)

But in the sentence, both words are in the instrumental case, so their forms change:

• narzeczona → narzeczoną
• narzeczony → narzeczonym

So:

• Ola is female → narzeczoną
• the speaker is male → narzeczonym

Because adjectives and possessive words in Polish must agree with the noun they describe in:

• gender
• number
• case

Here, moją goes with narzeczoną, so it also has to be feminine singular instrumental.

Compare:

• nominative: moja narzeczona
• instrumental: moją narzeczoną

This kind of matching is very important in Polish grammar.

Because jej here means her, and this possessive form does not change.

So:

• jej narzeczony = her fiancé
• jej narzeczonym = her fiancé in the instrumental context

Notice that jej stays the same, while the noun changes:

• narzeczony → narzeczonym

This is normal for jej. It is an indeclinable possessive form in this use.

In this sentence, a means something like:

• and
• while
• whereas

It links two clauses and gives a slight contrast or shift of perspective:

• Ola jest moją narzeczoną, a ja jestem jej narzeczonym.

So it is not just a simple joining word. It feels a bit like:

• Ola is my fiancée, and I am her fiancé
• or more literally in tone, Ola is my fiancée, while I am her fiancé

In many contexts, a is more natural than i when you are balancing two statements.

Not strictly necessary, because the verb jestem already tells you the subject is I.

So you could say:

• Ola jest moją narzeczoną, a jestem jej narzeczonym.

However, a ja jestem... sounds very natural because ja adds emphasis and symmetry:

• Ola is my fiancée, and I am her fiancé

It helps make the contrast clearer: Ola ... , and I ...

So ja is optional grammatically, but useful stylistically.

Almost, but not perfectly. A rough word-for-word breakdown is:

• Ola = Ola
• jest = is
• moją = my
• narzeczoną = fiancée
• a = and/while
• ja = I
• jestem = am
• jej = her
• narzeczonym = fiancé

The main thing that does not map neatly into English is the case system. English does not show the same noun and adjective changes here, but Polish does.

So the literal structure is close, but the grammar works differently underneath.

Usually yes. These words normally mean:

• narzeczona = fiancée
• narzeczony = fiancé

That is, someone you are formally engaged to marry.

If you just mean girlfriend or boyfriend, Polish would usually use:

• dziewczyna = girlfriend
• chłopak = boyfriend

So narzeczona / narzeczony is more specific than the English word partner.

Yes, Polish word order is fairly flexible, but the original sentence is very natural.

For example, you might also hear:

• Ola to moja narzeczona, a ja to jej narzeczony.
• Moją narzeczoną jest Ola, a jej narzeczonym jestem ja.

But these versions have different emphasis or style.

The original:

• Ola jest moją narzeczoną, a ja jestem jej narzeczonym.

is neutral, clear, and natural for learners to model.

Because Polish grammar requires gender marking much more often than English.

In this sentence, gender appears in:

• narzeczoną — feminine
• narzeczonym — masculine
• moją — feminine because it matches narzeczoną

English usually does not force this kind of agreement. Polish does, so learners often have to pay attention to whether the person being described is male or female, and then choose the right endings.