Ela não gosta de discutir temas políticos em público.

In Portuguese, the verb gostar almost always needs the preposition de before what you like.

Structure: gostar de + noun / verb (infinitive)

• Ela gosta de chocolate. – She likes chocolate.
• Ela gosta de discutir. – She likes to discuss.

So leaving out de (gosta discutir) is incorrect in standard Portuguese. You must say gostar de + discutir.

In Portuguese, the normal way to negate a verb is to put não directly before the conjugated verb:

• Ela não gosta… – She does not like…
• Eu não quero… – I do not want…

Putting não anywhere else (Ela gosta não de discutir…) is wrong or, at best, very unusual and marked. So the correct order is:

Ela não gosta de discutir…

In Portuguese, most adjectives come after the noun, unlike English:

• temas políticos – political topics
• livro interessante – interesting book
• filmes franceses – French movies

So temas políticos is the normal word order.
políticos temas sounds wrong or at least very poetic/old-fashioned.

Temas políticos is plural because we are talking about more than one political topic in general.

• tema político – a political topic (singular)
• temas políticos – political topics (plural)

Both are grammatically correct; the choice depends on meaning:

• Ela não gosta de discutir temas políticos em público.
  She doesn’t like to discuss political topics (in general) in public.

• Ela não gosta de discutir este tema político em público.
  She doesn’t like to discuss this political topic in public.

In Portuguese, every noun has a gender. Tema is masculine, even though it ends in -a (it’s an exception to the usual pattern).

• o tema / os temas – the topic / the topics (masculine)
• tema político / temas políticos – political topic / political topics

You mainly have to learn the gender with the noun:
o tema, o problema, o sistema, etc. are all masculine despite ending in -a.

The adjective políticos agrees with temas in gender (masculine) and number (plural).

In European Portuguese, discutir can mean both:

1. To discuss / talk about something seriously

   • discutir um tema na aula – to discuss a topic in class

2. To argue / quarrel (have a heated argument)

   • Eles discutiram ontem. – They argued yesterday.

In your sentence, discutir temas políticos em público usually suggests serious discussion/debate, but depending on context it can also suggest arguments about politics, because those often get heated.

Yes, you can, but there is a slight nuance:

• discutir temas políticos – to debate/discuss political topics (often more structured or serious, may imply argument)
• falar de política – to talk about politics (more general, can be casual conversation)

For example:

• Ela não gosta de falar de política em público.
  She doesn’t like to talk about politics in public.

This is perfectly natural and maybe even more common in everyday speech than discutir temas políticos.

Em público is a fixed expression meaning in public / in front of other people.

• Ela não gosta de discutir isso em público. – She doesn’t like to discuss this in public.

No público would literally be “in the audience” (em + o = no), referring to the group of people watching a show, speech, etc.:

• Ele está sentado no público. – He is sitting in the audience.

So for the meaning “in public”, always use em público, not no público.

Approximate European Portuguese pronunciation (not IPA):

• gosta de ≈ GOSH-tuh d(ɨ)
  
  • gosta – GOSH-tuh
  • de – a very short, reduced sound, like a quick “dɨ”

In fast speech, gosta de can sound almost like GOSH-tɨ.

• em público ≈ ẽ POO-blee-koo
  
  • em – nasal, like French “en”
  • público – stress on PU: POO-blee-koo

The written accents (público, políticos) show where the stress falls.

Gosta is 3rd person singular, present tense of gostar.

Present tense of gostar (European Portuguese):

• eu gosto – I like
• tu gostas – you like (informal singular)
• ele / ela gosta – he / she likes
• nós gostamos – we like
• vocês gostam – you like (plural)
• eles / elas gostam – they like

So Ela não gosta de… = She does not like to…

Yes, that’s correct and natural.

• Ela não gosta de discutir temas políticos em público.
  She doesn’t like to discuss political topics in public. (dislike)

• Ela odeia discutir temas políticos em público.
  She hates discussing political topics in public. (stronger feeling)

Odiar = to hate. The structure is the same:
odiar + infinitive → odeia discutir.

The sentence is neutral and perfectly natural in everyday European Portuguese.

You could hear it in:

• casual conversation
• a classroom or meeting
• written text (email, article, etc.)

It’s neither slangy nor overly formal; it’s standard, good Portuguese.