O întreb pe vânzătoare dacă brânza este proaspătă.

Here O is the unstressed direct-object pronoun meaning her. It refers to vânzătoare.

So Romanian is literally doing something like:

Her, I ask the saleswoman whether the cheese is fresh.

That sounds strange in English, but in Romanian this pronoun-before-the-verb pattern is very normal.

It is capitalized only because it is the first word of the sentence. In the middle of a sentence, it would be o.

Romanian object clitic pronouns normally come before the conjugated verb.

So:

• O întreb = I ask her
• not Întreb-o in this kind of neutral statement

Romanian does have forms like întreab-o!, but that is an imperative: ask her!

So in an ordinary statement, o before the verb is the expected position.

Yes, both refer to the same object, and this is a very common Romanian pattern called clitic doubling.

With a specific human direct object, Romanian often uses:

• a clitic pronoun: o
• plus the full noun phrase: pe vânzătoare

So O întreb pe vânzătoare is very natural Romanian.

In English we usually use only one:

• I ask the saleswoman
• or I ask her

Romanian often uses both together.

Pe marks a specific direct object, especially when it is a person or another animate being.

So in this sentence, vânzătoare is a specific person, and Romanian marks that with pe:

• pe vânzătoare

This pe usually does not translate directly into English. It is a grammar marker, not a separate meaning like on here.

A useful idea is:

• with people as direct objects, Romanian often uses pe
• especially when the person is specific or identifiable

With words for roles or professions, Romanian often uses the bare noun after pe when the person is understood from the situation:

• pe doctor
• pe profesoară
• pe vânzătoare

So pe vânzătoare can mean the saleswoman in context.

You may also encounter more explicitly definite forms in other contexts, but the version in your sentence is a very normal everyday way to refer to the person serving you.

Întreb is the 1st person singular present form of a întreba = to ask.

So:

• eu întreb = I ask
• tu întrebi = you ask
• el/ea întreabă = he/she asks

In your sentence, întreb tells you the subject is I, even though Romanian often leaves the subject pronoun eu unstated.

So O întreb... already means I ask her...

Dacă introduces an indirect yes/no question, so here it means if or whether.

The embedded question is:

• Este brânza proaspătă? = Is the cheese fresh?

When that becomes part of a larger sentence, Romanian uses dacă:

• O întreb ... dacă brânza este proaspătă.
• I ask ... whether the cheese is fresh.

So dacă here is not the conditional if of if it rains, I’ll stay home. It is the whether/if used for reported yes/no questions.

Brânza means the cheese. The -a at the end is the Romanian definite article attached to the noun.

So:

• brânză = cheese / a cheese
• brânza = the cheese

Romanian usually puts the definite article at the end of the noun, not before it like English does.

Because the adjective has to agree with brânza, which is feminine singular.

So:

• brânza = feminine singular
• proaspătă = feminine singular form of fresh

Compare:

• brânză proaspătă = fresh cheese
• lapte proaspăt = fresh milk
  because lapte is neuter/masculine-form singular, so the adjective is proaspăt

Romanian adjectives change form to match the noun’s gender and number.

Yes. Este and e both mean is.

• este is the full form
• e is shorter and very common in everyday speech

So both of these are natural:

• brânza este proaspătă
• brânza e proaspătă

The version with este can sound a little more careful or slightly more formal, but both are correct.

Romanian word order is fairly flexible, but some parts of this sentence follow strong patterns.

The most important fixed-ish pattern here is:

• the clitic pronoun o comes before the verb: O întreb

The rest can vary more depending on emphasis. For example, Romanian can often move parts around for focus, but the version you have is a very normal neutral sentence:

O întreb pe vânzătoare dacă brânza este proaspătă.

So as a learner, this is the safest order to remember.