La dottoressa dice che devo riposare.

In Italian, it is very common to use the definite article before a professional title or role when talking about a specific person:

• la dottoressa = the doctor
• il professore = the professor
• l’avvocato = the lawyer

So La dottoressa dice... sounds natural in Italian.

In some situations, especially when directly addressing someone, you would drop the article:

• Buongiorno, dottoressa.

But in a normal statement like this one, la dottoressa is standard.

Because dottoressa is the feminine form of dottore.

• il dottore = male doctor
• la dottoressa = female doctor

Italian usually marks gender more clearly than English does. Since the doctor here is female, dottoressa is used.

Dice is the present indicative of dire (to say / to tell).

Its basic forms are:

• io dico = I say
• tu dici = you say
• lui/lei dice = he/she says

So La dottoressa dice literally means The doctor says.

Che here means that and introduces the second clause:

• La dottoressa dice = The doctor says
• che devo riposare = that I must rest

English often drops that:

• The doctor says (that) I need to rest.

Italian usually keeps che in this kind of sentence, so it is very normal and expected here.

Italian often leaves out subject pronouns when they are clear from the verb ending.

• devo already means I must / I have to
• so io is not necessary

You can add io for emphasis or contrast:

• Io devo riposare, non tu.
  I have to rest, not you.

But in a neutral sentence, devo by itself is enough.

After modal verbs like dovere (must / have to), Italian uses an infinitive.

So:

• devo riposare = I must rest

This is the same pattern as:

• voglio mangiare = I want to eat
• posso entrare = I can enter
• devi studiare = you have to study

Riposo is a noun or a different verb form, not the infinitive needed here.
The correct infinitive is riposare.

Devo is the first person singular present indicative of dovere.

• dovere = to have to / must
• devo = I have to / I must

In this sentence, it expresses necessity or obligation:

• devo riposare = I need to rest / I have to rest / I must rest

Because it is an infinitive, and after devo it stays in the infinitive form.

Italian does this after modal verbs:

• devo riposare = I must rest
• puoi venire = you can come
• vuole parlare = he/she wants to speak

Only the modal verb changes for person and tense. The second verb usually remains in the infinitive.

Yes, but the meaning would shift slightly.

• La dottoressa dice che devo riposare.
  The doctor says that I need to rest.
  This sounds present and current.

• La dottoressa ha detto che devo riposare.
  The doctor said that I need to rest.
  This refers to something she said earlier.

So both are possible, but dice focuses on the present statement, while ha detto points to a past moment.

Italian word order is often similar to English, but it is more flexible. In this sentence, the structure is:

• La dottoressa = subject
• dice = verb
• che = connector
• devo riposare = subordinate clause

Inside the second clause, Italian normally does not need the subject pronoun:

• che devo riposare = that I must rest

If you say che io devo riposare, it is still grammatical, but it adds emphasis. The version without io is the most natural here.

In this sentence, dice is closer to says.

• La dottoressa dice che... = The doctor says that...

Italian dire can correspond to both say and tell, depending on the structure.

For example:

• dice che devo riposare = says that I must rest
• mi dice di riposare = tells me to rest

So in your sentence, because it is followed by che + clause, says is the best match.

Yes. That would mean:

• The doctor tells me / says to me that I need to rest

The mi adds the indirect object to me.

Without mi, the sentence is still perfectly fine, because Italian does not always need to state the listener if it is obvious or unimportant.

So:

• La dottoressa dice che devo riposare. = natural and general
• La dottoressa mi dice che devo riposare. = emphasizes that she is saying it to me

Not exactly.

• riposare = to rest
• riposarsi = to rest oneself

In everyday Italian, riposare is very common and natural in sentences like this:

• Devo riposare.

You may also hear riposarmi in some contexts:

• Devo riposarmi un po’. = I need to rest a bit.

But in your sentence, riposare is completely normal and standard.

Normally, no. In standard Italian, job titles and common nouns are usually not capitalized unless they begin the sentence.

So:

• La dottoressa dice che devo riposare. ✅

You would capitalize it only for special stylistic reasons or in a formal heading, not in ordinary running text.