Learn Hardcore Portuguese (Portugal): Eu demonstro confiança.

It translates as "I demonstrate confidence" (or "I exude confidence"). The sentence expresses that the speaker actively shows or conveys confidence through their behavior.

What is the grammatical structure of the sentence, particularly the verb "demonstro"?

"Demonstro" is the first person singular form of the verb demonstrar in the present indicative tense. The subject Eu (I) is explicitly stated, which is common for emphasis even though Portuguese often allows the subject pronoun to be omitted when the verb conjugation clearly indicates it.

Why is there no article before the noun confiança in this sentence?

In Portuguese, abstract qualities such as confiança (confidence) are often used without an article when referring to a general state or quality. This omission emphasizes that you are speaking about confidence in an abstract, overall sense rather than a specific instance or defined quantity.

Is there a difference in nuance between using "demonstro" and a more general verb like "mostro"?

Yes. While both demonstrar and mostrar can translate as "to show," demonstrar implies that the quality is visibly exhibited through actions or behavior—it carries a sense of substantiating or conveying something internally held. Mostrar is broader and may simply refer to making something visible without the connotation of actively embodying that quality.