Minha filha gosta de suco de manga, mas eu prefiro comer melão gelado.

Because filha is a feminine noun, so the possessive has to match it:

• meu filho = my son
• minha filha = my daughter

In Portuguese, possessives agree with the thing/person owned, not with the speaker.

Yes. In Brazilian Portuguese, both are possible:

• minha filha
• a minha filha

With possessives, Brazilian Portuguese often allows the article to be optional, especially in everyday speech.
So this sentence sounds natural either way:

• Minha filha gosta...
• A minha filha gosta...

The version without the article is very common and natural.

The verb gostar normally requires the preposition de.

So:

• gostar de suco = to like juice
• gostar de manga = to like mango
• gostar de viajar = to like traveling

That means:

• Minha filha gosta de suco de manga

is correct, while gosta suco is not.

This is something you usually just have to memorize with the verb: gostar de.

Because de + noun is commonly used to show flavor, type, or ingredient.

• suco de laranja = orange juice
• sorvete de chocolate = chocolate ice cream
• bolo de cenoura = carrot cake

So suco de manga means mango juice.

If you said suco da manga, it would sound more like juice from the mango in a very specific sense, not the normal way to name the drink.

Yes, manga has two common meanings:

• manga = mango
• manga = sleeve

Context tells you which one it means.

In suco de manga, it clearly means mango, because sleeve juice would not make much sense.

Yes, mas prefiro would also be grammatically correct.

Portuguese often drops subject pronouns because the verb ending already shows the subject:

• prefiro already means I prefer

But eu is often added for contrast or emphasis. Here, it helps highlight the difference:

• Minha filha gosta... mas eu prefiro...
• My daughter likes..., but I prefer...

So eu makes the contrast stronger and more natural.

Yes, both are possible, but they mean slightly different things.

• prefiro comer melão gelado = I prefer to eat chilled melon
• prefiro melão gelado = I prefer chilled melon

The version with comer explicitly says the action: to eat.

That works especially well here because the first part talks about juice and the second part contrasts it with eating melon.

Also, preferir can be followed by:

• a noun: prefiro café
• an infinitive: prefiro comer
• one option over another: prefiro X a Y

In Portuguese, adjectives often come after the noun:

• melão gelado = chilled melon
• casa grande = big house
• carro novo = new car

Putting the adjective after the noun is the most normal pattern.

Also, gelado agrees with melão, which is masculine singular:

• melão gelado
• manga gelada
• melões gelados

Because melão is a masculine noun.

Adjectives in Portuguese usually agree in gender and number with the noun they describe:

• melão gelado = chilled melon
• melancia gelada = chilled watermelon
• frutos gelados = chilled fruits

Since melão is masculine singular, the adjective is gelado.

They are present tense forms:

• gosta = he/she likes
• prefiro = I prefer

More specifically:

gostar

• eu gosto
• você/ele/ela gosta

preferir

• eu prefiro
• você/ele/ela prefere

So in the sentence:

• Minha filha gosta... = My daughter likes...
• eu prefiro... = I prefer...

With melão (melon), comer is the natural verb because you eat it.

• comer melão = to eat melon

For juice, the normal verbs would be:

• beber suco = to drink juice
• tomar suco = to have/drink juice

In Brazil, tomar suco is extremely common in everyday speech.

So the sentence contrasts:

• the daughter likes mango juice
• the speaker prefers eating chilled melon

The accent mark shows both stress and helps signal the vowel pattern.

• melão is stressed on the last syllable: me-LÃO
• The ão sound is a very common Portuguese nasal ending

This ending appears in many words:

• pão = bread
• limão = lemon
• melão = melon

English speakers often need practice with ão, because it is nasal and does not sound exactly like any normal English ending.

Yes, in standard writing, a comma before mas is normal and expected.

• ..., mas eu prefiro...

Here mas means but, and it connects two contrasting clauses.
Using the comma is the standard punctuation choice.

Yes. A few natural variations are:

• Minha filha gosta de suco de manga, mas eu prefiro melão gelado.
• A minha filha gosta de suco de manga, mas eu prefiro comer melão gelado.
• Minha filha gosta de tomar suco de manga, mas eu prefiro comer melão gelado.

These all sound natural, with small differences in emphasis:

• tomar suco emphasizes having/drinking juice
• comer emphasizes the act of eating
• adding a before minha filha is also fine in Brazilian Portuguese