Volim zdravu hranu, npr. voće i povrće.

Because Croatian usually leaves out the subject pronoun when the verb already makes it clear who the subject is. Volim is a 1st person singular verb form, so it already means I like / I love.

You can add ja if you want emphasis or contrast:

• Ja volim zdravu hranu, a on ne. = I like healthy food, but he does not.

It can mean either, depending on context. The verb voljeti covers both ideas.

• With things such as food, music, sports, etc., English usually translates it as like:
  Volim zdravu hranu. = I like healthy food.
• With people, it often means love:
  Volim te. = I love you.

Because it is the direct object of volim. In Croatian, the direct object usually goes in the accusative case.

So:

• hrana = nominative singular, basic dictionary form
• hranu = accusative singular

That is why you say Volim hranu and not Volim hrana.

Because adjectives in Croatian must agree with the noun they describe in gender, number, and case.

Here, hranu is:

• feminine
• singular
• accusative

So the adjective must match it:

• zdrava hrana = healthy food
• zdravu hranu = healthy food as a direct object

Croatian does not have articles. So nouns appear without words like a, an, or the.

That means:

• hrana can mean food, the food, or sometimes some food
• voće can mean fruit or the fruit
• povrće can mean vegetables or the vegetables, depending on context

Croatian usually relies on context instead of articles.

npr. stands for na primjer, which means for example.

So:

• Volim zdravu hranu, npr. voće i povrće.
• Volim zdravu hranu, na primjer voće i povrće.

Both mean the same thing.

Because npr. voće i povrće is an added example that explains zdravu hranu more specifically. The comma marks that extra explanatory part.

This is similar to English punctuation with for example.

Because in Croatian, voće and povrće are usually treated as collective or mass nouns.

They refer to these things in a general sense:

• voće = fruit
• povrće = vegetables / vegetable food

So Croatian often uses these singular-looking forms where English also often speaks generally:

• Jedem voće. = I eat fruit.
• Jedem povrće. = I eat vegetables.

In function, yes: they are examples of the kind of food being liked. But the form does not visibly change here.

That is because voće and povrće are neuter singular, and in neuter singular the nominative and accusative forms are the same:

• nominative: voće, povrće
• accusative: voće, povrće

So even though they fit the object role, they look unchanged.

A rough guide is:

• voće ≈ VO-cheh
• povrće ≈ PO-vr-cheh

A few helpful notes:

• ć is a soft sound, softer than English ch
• in povrće, the r is pronounced clearly and can almost act like the center of a syllable
• č and ć are different letters in Croatian, although many beginners hear them as similar at first

Yes. Croatian word order is more flexible than English.

The sentence Volim zdravu hranu, npr. voće i povrće. is the most neutral and natural order for a learner.

But you can move parts around for emphasis:

• Zdravu hranu volim. = emphasis on healthy food
• Voće i povrće volim. = emphasis on fruit and vegetables

So the meaning can stay similar, while the focus changes.