A dentista disse que eu preciso mastigar devagar por alguns dias.

No. Dentista can refer to either a man or a woman. The article tells you the gender of the person:

• a dentista = the female dentist
• o dentista = the male dentist

This is common with some profession words in Portuguese. Even though dentista ends in -a, it is not automatically feminine.

In Portuguese, it is very normal to use a definite article before a specific person or profession when they are the subject of the sentence.

So A dentista disse... sounds natural and complete.

Leaving the article out, as in Dentista disse..., would usually sound unnatural in normal speech.

Yes. Disse is the preterite form of dizer and means said.

This verb is irregular:

• eu digo = I say
• ela disse = she said

So you cannot build it in a regular way. It is not dizeu or anything similar; the correct past form is disse.

Both can work in many situations, but disse is the most direct match for said when you are reporting words or information.

• A dentista disse que... = The dentist said that...
• A dentista falou que... is also common in Brazilian Portuguese, especially in speech

Very roughly:

• dizer focuses more on what was said
• falar often focuses more on speaking/talking

So disse que is a very natural choice here.

Here que introduces the reported statement, like that in English:

• disse que eu preciso... = said that I need...

In English, that is often omitted:

• The dentist said I need...

In Portuguese, que is usually kept. Omitting it would sound much less natural.

This is a very common point for English speakers.

Portuguese does not always shift the tense backward the way English often does in reported speech. If the statement is still true now, Portuguese can keep the present:

• A dentista disse que eu preciso mastigar devagar...

This suggests the dentist said it in the past, but the need still applies now.

If you said precisava, that would sound more tied to the past viewpoint:

• A dentista disse que eu precisava...

That version is also possible in some contexts, but preciso is very natural when the advice is still valid.

Yes, it could.

Portuguese often drops subject pronouns when the verb already makes the subject clear. Since preciso clearly means I need, you can say:

• A dentista disse que preciso mastigar devagar...

Adding eu is also fine. It can make the sentence a little clearer or more explicit:

• A dentista disse que eu preciso...

So both are natural.

Because precisar has two common patterns:

• precisar + infinitive = to need to do something
  
  • preciso mastigar = I need to chew
• precisar de + noun = to need something
  
  • preciso de ajuda = I need help

So in this sentence, the standard structure is:

• eu preciso mastigar

not eu preciso de mastigar.

Devagar is an adverb, and here it tells you how the action should be done.

• mastigar devagar = to chew slowly

Yes, this word order is very normal in Portuguese: verb + adverb.

You could also hear:

• mastigar mais devagar = to chew more slowly

A more formal synonym is lentamente, but devagar is extremely common and natural in everyday Brazilian Portuguese.

Because por is commonly used to express duration of time.

• por alguns dias = for a few days

Here it means the situation will last during that time period.

Para usually has other meanings, such as:

• destination
• purpose
• deadline
• intended recipient

So por alguns dias is the natural choice for duration.

Both can refer to a few days, but they are not exactly the same in tone.

• alguns dias = some days / a few days
• uns dias = a few days, often a bit more informal or looser

In this sentence, por alguns dias sounds clear and standard.

Also, there is no article before alguns dias because alguns already works as a determiner. You do not need os or uns with it.