A mia sorella piace il pollo al forno con le patate.

Because piacere does not work like English to like.

Italian structures it more like:

• Something is pleasing
• to someone

So in this sentence:

• il pollo al forno con le patate = the thing that is pleasing
• a mia sorella = to my sister

Literally, the structure is closer to:

To my sister, baked chicken with potatoes is pleasing.

If you say Mia sorella piace, that means My sister is pleasing / likable, which is a completely different idea.

Here a marks the person who experiences the liking.

With piacere, the person is usually introduced by a:

• A me piace = I like
• A te piace = you like
• A mia sorella piace = my sister likes

So a here often corresponds to English to in the more literal structure is pleasing to.

With singular family members, Italian usually omits the article before the possessive:

• mia sorella = my sister
• mio fratello = my brother
• mia madre = my mother

So a mia sorella is the normal form.

But the article often comes back if:

• the family noun is plural: alle mie sorelle
• the noun is modified: alla mia sorella maggiore
• you use certain special forms or regional usage

So here, a mia sorella is exactly what you would expect.

Because the verb agrees with the thing that is liked, not with the person.

The thing liked here is:

il pollo al forno con le patate

The main noun is il pollo, which is singular, so the verb is singular:

• piace = singular
• piacciono = plural

Even though patate is plural, the whole phrase is understood as one dish: baked chicken with potatoes.

Compare:

• A mia sorella piace il pollo al forno con le patate.
  My sister likes baked chicken with potatoes.
  → one dish, so piace

• A mia sorella piacciono il pollo al forno e le patate.
  My sister likes baked chicken and potatoes.
  → two separate things, so piacciono

Yes. Le can replace a mia sorella.

So you can say:

• A mia sorella piace il pollo al forno con le patate.
• Le piace il pollo al forno con le patate.

Both are correct.

A useful point:

• a mia sorella = full phrase, more explicit
• le = indirect object pronoun, meaning to her

You may also hear both together in spoken Italian:

• A mia sorella le piace...

That kind of doubling is common in speech and in some regional varieties, but if you are learning standard neutral Italian, the safest choices are:

• A mia sorella piace...
• Le piace...

Italian uses articles more often than English.

In this sentence, il pollo is the subject of piace, so the article is natural and expected.

Italian often says:

• Mi piace il caffè.
• Ti piace la musica.
• Le piacciono i libri.

Even where English might sometimes say just coffee, music, or books, Italian often prefers the article.

So il pollo al forno is normal Italian here.

Al forno means baked or more literally in the oven / oven-baked.

It is made from:

• a + il = al
• forno = oven

So:

• pollo al forno = baked chicken / chicken cooked in the oven

You will see this pattern in many food expressions:

• pasta al forno = baked pasta
• verdure al forno = roasted/baked vegetables

In this sentence, con le patate is most naturally understood as part of the dish:

baked chicken with potatoes

So the sentence is not mainly listing two separate things she likes. It is describing one meal or one preparation.

That is why piace stays singular.

If you wanted to clearly say she likes both chicken and potatoes as separate items, you would usually say something like:

A mia sorella piacciono il pollo al forno e le patate.

So in your sentence, con le patate is best read as served/cooked with potatoes.

Because Italian often uses the definite article with nouns in places where English would not.

So con le patate is perfectly normal Italian for with potatoes.

English often drops the article in food expressions, but Italian frequently keeps it:

• con le patate = with potatoes
• con il riso = with rice
• con la salsa = with sauce

So this is not unusual at all; it is just a normal article pattern in Italian.

Yes. Italian allows some flexibility.

You can also say:

Il pollo al forno con le patate piace a mia sorella.

That has the same basic meaning.

The version with a mia sorella first is very natural because it highlights the person:

A mia sorella piace... = My sister likes...

This word order is especially common with piacere, since speakers often mention the person first and then the thing liked.