A mi hija le encantan las natillas de vainilla.

Yes, they both point to the same person, but they do different jobs in the sentence.

• le is the indirect object pronoun required by verbs like gustar and encantar.
• a mi hija is the clarifying/emphasizing phrase that tells us exactly who le refers to.

Spanish very often uses both together:

• Le encanta = she/he loves it
• A mi hija le encanta = my daughter loves it

So the pronoun is not optional just because the full noun is there. In this kind of structure, Spanish normally keeps the pronoun and adds the a + person phrase for clarity or emphasis.

Because las natillas de vainilla is plural.

With encantar, the verb agrees with the thing that is pleasing, not with the person who feels the pleasure.

So:

• Me encanta el chocolate. → el chocolate is singular
• Me encantan las natillas. → las natillas is plural

In your sentence, the subject is:

• las natillas de vainilla

Since that is plural, the verb must be plural too:

• encantan

The subject is las natillas de vainilla.

That can feel strange to an English speaker, because in English we usually structure it like:

• My daughter loves vanilla custard.

But Spanish is built more like:

• Vanilla custards are delightful to my daughter.

So grammatically:

• A mi hija = indirect object
• le = indirect object pronoun
• encantan = verb
• las natillas de vainilla = subject

That is why the verb matches las natillas, not mi hija.

Because a mi hija is an indirect object phrase.

With verbs like gustar, encantar, interesar, and similar verbs, the person affected is introduced with a:

• A Juan le gusta el café.
• A mi hija le encantan las natillas.

This a is not the same as the personal a used for direct objects, although it may look similar. Here it marks the person who receives the feeling or experience.

Yes. In Spain, natillas is normally used in the plural to refer to the dessert.

Even though English often uses a singular mass noun like custard, Spanish commonly says:

• las natillas

So this is completely natural Spanish. The singular natilla exists, but natillas is the usual way to name the dessert in general.

That is also why you have:

• las natillas
• encantan (plural)

Because de + noun is a very common way in Spanish to describe flavour, type, or material.

So:

• helado de chocolate
• yogur de fresa
• natillas de vainilla

This is often more natural than trying to turn the flavour word into an adjective.

So natillas de vainilla simply means vanilla custard or vanilla-flavoured custard.

Yes. Encantar follows the same grammar pattern as gustar.

Compare:

• A mi hija le gustan las natillas. = she likes the custards
• A mi hija le encantan las natillas. = she loves the custards

In both cases:

• the experiencer is the indirect object
• the verb agrees with the thing liked/loved

So if you understand gustar, this sentence works the same way. The main difference is intensity:

• gustar = to like
• encantar = to love / to be delighted by

Yes. Spanish word order is flexible here.

These are all possible:

• A mi hija le encantan las natillas de vainilla.
• Le encantan las natillas de vainilla a mi hija.
• Las natillas de vainilla le encantan a mi hija.

The most neutral version is often the original one, especially when introducing the person first.

Changing the order can shift emphasis:

• A mi hija... emphasizes my daughter
• Las natillas de vainilla... emphasizes the dessert

But the grammar stays the same.

Yes, if it is already clear who le refers to.

For example, in conversation, if everyone knows you are talking about your daughter, you can simply say:

• Le encantan las natillas de vainilla.

But if the listener might not know who le means, then a mi hija makes it clear.

So:

• le = enough when context is clear
• a mi hija le = clearer and often more emphatic

No. That would be ungrammatical for this meaning.

Encantar does not work like the English verb to love in this sentence. You cannot normally say:

• Mi hija encanta X

to mean my daughter loves X.

Instead, Spanish uses the gustar-type structure:

• A mi hija le encantan las natillas de vainilla.

A sentence like X encanta a Y means X delights Y. So the thing causing delight is the subject.

For example:

• Las natillas encantan a mi hija.

That is grammatically possible, though less natural than the version with le and the usual word order.

Because mi hija is not the direct object here; she is the indirect object.

Spanish indirect object pronouns are:

• me
• te
• le
• nos
• os
• les

So for to my daughter, you need le.

la would be a direct object pronoun, which is not what this sentence needs.

So:

• le = to her
• la = her

In this structure, the person is the one experiencing the liking, so Spanish uses the indirect-object form: le.