Mi dica se per Natale preferisce un libro o una sciarpa.

Mi dica means Tell me or Please tell me.

A few useful details:

• dire = to say / to tell
• dica is the formal command form, used with Lei
• mi = to me

So Mi dica is literally Tell me, addressed politely to one person.

Because in Italian, object pronouns like mi, ti, lo, la, etc. usually come before a conjugated verb.

So:

• Mi dica = Tell me (formal)
• not Dica mi

There is a useful contrast with the informal positive imperative:

• Dimmi = Tell me (informal, to one person)
• Mi dica = Tell me (formal)

So pronoun placement changes depending on the form being used.

It is formal.

You can tell because of:

• dica
• preferisce

Both refer to the polite Lei form.

An informal version would be:

• Dimmi se per Natale preferisci un libro o una sciarpa.

So the original sentence is what you might say to someone you want to address politely.

Here se means if / whether and introduces an indirect question.

So:

• Mi dica se... = Tell me if / whether...

This is not a condition like If it rains, we stay home.
Instead, it introduces a question embedded inside the sentence:

• Do you prefer a book or a scarf for Christmas?
• becomes
• Tell me if/whether you prefer a book or a scarf for Christmas.

That is a very common use of se in Italian.

Because after Mi dica se..., Italian normally uses the indicative in a sentence like this.

So:

• Mi dica se preferisce... = correct

Here the speaker is asking for factual information about the person's preference, so preferisce is natural.

English speakers sometimes expect a subjunctive after expressions like tell me if, but Italian does not usually use the subjunctive here.

Per Natale usually means for Christmas.

In context, it can suggest:

• as a Christmas gift
• for Christmas time
• for Christmas in general

So in this sentence, it most naturally means:

• for Christmas
• as in Which would you prefer for Christmas: a book or a scarf?

Because holidays in Italian often appear without an article.

So you say:

• a Natale = at Christmas
• per Natale = for Christmas

not usually:

• per il Natale

The version without the article is the normal one in this kind of sentence.

Because libro is masculine and sciarpa is feminine.

So the indefinite articles are:

• un libro = a book
• una sciarpa = a scarf

This is just normal gender agreement:

• masculine singular noun → un
• feminine singular noun → una

The subject is the implied Lei.

Italian often leaves subject pronouns out when the verb already makes the subject clear.

So:

• preferisce = you prefer in the formal Lei form

You could say Lei preferisce, but it is usually unnecessary unless you want emphasis or contrast.

Yes. O is the normal, simple word for or.

So:

• un libro o una sciarpa = a book or a scarf

You could also use oppure, which can sound a little more explicit:

• un libro oppure una sciarpa

But in this sentence, o is completely natural.

Yes. For example:

• Mi dica se preferisce un libro o una sciarpa per Natale.

This is also natural.

The original version:

• Mi dica se per Natale preferisce un libro o una sciarpa.

places per Natale earlier, which slightly highlights the Christmas context before the choice is mentioned.

Both word orders are possible; the difference is mainly one of emphasis and style, not basic meaning.

Yes, but it is a polite command/request, not a harsh order.

In Italian, this form is very often used to make a request in a courteous way. Depending on tone and context, Mi dica can feel like:

• Tell me
• Please tell me
• Let me know

So grammatically it is an imperative/request form, but pragmatically it is often quite polite.