How do Brazilians use nossa?

Brazilians start a sentence with Nossa, when something surprises them: the time, how tired they are, a mistake, a lost key. These are lines from the course:

PortugueseMeaningIn CiaoSpeak
Nossa, que horas são?Gosh, what time is it? (Ana, at the language exchange)Speak: Language exchange
Nossa, estou tão cansado esta semana! O que eu faço?Gosh, I'm so tired this week! What do I do?Speak: New job
Nossa, cadê a minha chave? Você viu?Gosh, where's my key? Have you seen it?Speak: New job
Nossa, que buraco enorme ali na rua! Você viu?Gosh, what a huge pothole there on the street! Have you seen it?Speak: Your neighbor
Nossa, desculpe! A gente resolve isso agora.Oh no, I'm sorry! We'll sort it out right away.Speak: Returning a shirt

Is nossa rude or religious?

No. Nossa! comes from Nossa Senhora! ("Our Lady!"), but today it's just "wow", fine with anyone, including at work. Nossa Senhora! in full is a stronger "good heavens!".

PortugueseMeaning
Nossa, que lindo!Wow, how beautiful!
Nossa Senhora!Good heavens! (stronger)

What does nossa mean as "our"?

As a regular word, nossa means "our" before a feminine noun, and nosso before a masculine one: a nossa casa, o nosso carro.

PortugueseMeaningIn CiaoSpeak
Esta é a Júlia, nossa nova gerente.This is Júlia, our new manager.Unit 9
o nosso carroour carNot in the course

How can you practice Brazilian Portuguese out loud?

Practice it in short, real exchanges, out loud. CiaoSpeak's Brazilian Portuguese course teaches everyday words like Nossa! with a recording in a Brazilian accent, and in the Speak tab people across Brazil (a São Paulo baker, a Rio ride-app driver, your language-exchange partner Ana) ask you one question at a time. You answer by voice or typing, and the app tells you whether a Brazilian would understand you. Lessons are free; in the Speak tab, today's questions (up to five a day) are free too, and CiaoSpeak+ adds practice in any scene whenever you like. More words like this one: the Brazilian slang list.