Ana quer provar a sobremesa, mas eu prefiro uma fatia de pão com manteiga.

Yes. Provar has more than one meaning in Portuguese. Common meanings include:

• to taste / try food
• to try on clothes
• to prove something

In Ana quer provar a sobremesa, the food context makes it mean to taste or to try the dessert.

Examples:

• Quero provar o bolo. = I want to taste the cake.
• Preciso provar que estou certo. = I need to prove that I’m right.
• Ela vai provar o vestido. = She is going to try on the dress.

In Brazilian Portuguese, provar when it means to taste is usually a direct transitive verb, so it normally takes a direct object with no preposition:

• provar a sobremesa
• provar o molho
• provar o café

So Ana quer provar a sobremesa is the normal structure.

You may sometimes hear other expressions such as experimentar for to try/taste, but with provar, no de is needed here.

Portuguese uses definite articles more often than English does. In this sentence, a sobremesa can mean:

• the dessert in a specific situation, such as the dessert being served
• sometimes more naturally in English, just dessert

So even if English might say Ana wants to try dessert, Portuguese often prefers a sobremesa.

This is very common:

• Vou para a escola. = I’m going to school.
• Ela gosta do café. = She likes coffee.

Portuguese often sounds more natural with the article where English may omit it.

Quer is the third-person singular present tense of querer:

• eu quero = I want
• você / ele / ela quer = you/he/she wants
• nós queremos = we want
• eles / elas querem = they want

Since the subject is Ana, we use quer:

• Ana quer provar a sobremesa.

Prefiro is the first-person singular present tense of preferir:

• eu prefiro = I prefer
• você / ele / ela prefere
• nós preferimos
• eles / elas preferem

So eu prefiro means I prefer.

Also notice that preferir is an -ir verb, and in the eu form it changes:

• preferir → prefiro

This kind of vowel change is normal in some Portuguese verbs.

Portuguese often drops subject pronouns because the verb ending already shows the subject. So prefiro alone already means I prefer.

However, eu is included here for contrast or emphasis:

• Ana quer... mas eu prefiro...

That gives a feeling like:

• Ana wants..., but I prefer...

So eu is not required, but it is very natural when contrasting one person with another.

Uma fatia de pão means a slice of bread.

• fatia = slice
• pão = bread

Using fatia makes the quantity more specific. Compare:

• prefiro pão com manteiga = I prefer bread with butter
• prefiro uma fatia de pão com manteiga = I prefer a slice of bread with butter

So the sentence is being more precise.

In Portuguese, many quantity expressions use de:

• uma fatia de pão = a slice of bread
• um copo de água = a glass of water
• uma xícara de café = a cup of coffee
• um pedaço de bolo = a piece of cake

So de links the measure word (fatia) to the thing being measured (pão).

In pão com manteiga, Portuguese commonly leaves out the article because manteiga is being treated as a general food accompaniment or ingredient.

So:

• pão com manteiga = bread with butter

This sounds natural and idiomatic.

You could sometimes hear com a manteiga in a different context, but that would usually refer to a more specific butter, as in with the butter. In this sentence, the general version com manteiga is the natural choice.

Yes, often it could.

• Ana quer provar a sobremesa.
• Ana quer experimentar a sobremesa.

Both can mean Ana wants to try the dessert.

A small difference:

• provar strongly suggests tasting
• experimentar can mean to try more generally

With food, both are common, but provar is especially natural for tasting something.

Pão is one of the words learners often find tricky because of ão.

A helpful rough guide is:

• pão sounds somewhat like powng, but with a nasal ending, not a full ng

Important points:

• The ã is nasal
• The o is not pronounced as a strong separate vowel the way it would be in English

The ending ão is very common in Portuguese:

• pão
• não
• coração

If you are learning Brazilian Portuguese pronunciation, mastering ão is very useful.

Usually, yes. Sobremesa is the standard word for dessert in Portuguese.

It literally has the idea of something that comes after the meal, but in normal usage it simply means dessert.

Examples:

• Qual é a sobremesa? = What is the dessert?
• A sobremesa está ótima. = The dessert is great.

Yes, but the original sentence uses a very normal and natural word order:

• Ana quer provar a sobremesa, mas eu prefiro uma fatia de pão com manteiga.

Portuguese allows some flexibility, but changing the order can change emphasis or make the sentence sound less neutral.

For a learner, the original structure is an excellent standard pattern:

• subject + verb + object
• mas + subject + verb + object

So this sentence is a good model to copy when building your own sentences.