Ŝi preferas rizon kun tomatoj, sed mia frato volas terpomojn kun viando.

In Esperanto, -as marks the present tense. So:

• preferas = prefers / is preferring
• volas = wants

The verb ending does not change with the subject, so:

• mi preferas
• ŝi preferas
• ili preferas

all use -as if the action is in the present.

The ending -n marks the direct object in Esperanto.

In this sentence:

• Ŝi preferas rizon → rizon is what she prefers
• mia frato volas terpomojn → terpomojn is what he wants

So both get -n.

But kun tomatoj and kun viando are prepositional phrases with kun (with), not direct objects. After kun, you normally do not use -n.

So:

• rizon = direct object
• terpomojn = direct object
• tomatoj = object of the preposition kun
• viando = object of the preposition kun

Because Esperanto marks number very regularly:

• -o = singular noun
• -oj = plural noun
• -on = singular direct object
• -ojn = plural direct object

So:

• terpomojn = potatoes as a direct object
• viando = meat, singular

The reason viando is singular is that meat is usually treated as an uncountable noun, just like in English. You normally say meat, not meats, unless you mean kinds of meat.

Because mia is the possessive form meaning my.

In Esperanto, the -a ending is used for words that function like adjectives, including possessives:

• mia = my
• via = your
• lia = his
• ŝia = her
• nia = our

So mia frato means my brother.

The form mio is not used for my. A noun ending in -o would be a thing, not a possessive adjective.

Kun means with.

It links the main food to what comes with it:

• rizon kun tomatoj = rice with tomatoes
• terpomojn kun viando = potatoes with meat

It is simply a preposition. As in most Esperanto sentences, the noun after a preposition does not take -n unless there is some special reason.

Esperanto has no indefinite article.

So:

• rizo can mean rice
• terpomoj can mean potatoes
• frato can mean a brother or just brother, depending on context

Esperanto only has a definite article, la, meaning the.

So if you wanted to say the brother, you would say la frato. But here mia frato already means my brother, so la is unnecessary.

A few pronunciation points help here:

• ŝ is pronounced like English sh
  • ŝi sounds like shee
• j is pronounced like English y
• oj sounds like oy
• Stress in Esperanto is always on the second-to-last syllable

So:

• ŝi = shee
• tomatoj = to-ma-TOY, with stress on ma
• terpomojn = ter-po-MOYN, with stress on po

More exactly, terpomojn breaks down as:

• terpom- = potato
• -o- = noun
• -j- = plural
• -n = direct object

Yes, Esperanto word order is fairly flexible, especially because the -n ending shows the direct object.

The basic order here is very natural:

• Ŝi preferas rizon
• mia frato volas terpomojn

But you could rearrange parts for emphasis, for example:

• Rizon ŝi preferas
• Terpomojn volas mia frato

That said, for learners, the normal subject–verb–object order is usually the safest and clearest choice.

Because sed means but, while kaj means and.

This sentence contrasts two different preferences:

• she prefers one thing,
• but my brother wants another.

So sed is the natural connector for contrast.

Yes, very similarly.

Here:

• Ŝi preferas rizon kun tomatoj = she prefers rice with tomatoes

So preferi takes a direct object, just like English prefer:

• Mi preferas teon. = I prefer tea.
• Ili preferas panon. = They prefer bread.

In this sentence, that is why rizon gets the direct-object ending -n.