Is the word falamos the same in Brazilian and European Portuguese?

Yes

The word "falamos" is identical in meaning, grammar, and spelling in both Brazilian and Continental Portuguese. The only difference lies in pronunciation.

In Brazilian Portuguese, the unstressed vowels are generally more "open" and clearly articulated. When a Brazilian says "falamos," the "a" sounds are more distinct. In Continental Portuguese, unstressed vowels undergo "vowel reduction," meaning they are often shortened or "swallowed," making the word sound more like "flamos" to an untrained ear.

Brazilian Portuguese Examples

1. Nós falamos muito sobre isso ontem. (We talked about this a lot yesterday.)
2. Falamos com o professor depois da aula. (We spoke with the professor after class.)
3. A gente... (no, must use 'falamos') ... Nós falamos português e espanhol. (We speak Portuguese and Spanish.)
4. Falamos sobre o novo projeto na reunião. (We talked about the new project at the meeting.)
5. Sempre falamos a verdade para os nossos amigos. (We always tell the truth to our friends.)

Continental Portuguese Examples

1. Nós falamos português com naturalidade. (We speak Portuguese naturally.)
2. Falamos com o senhor médico agora mesmo. (We spoke with the doctor just now.)
3. Nós falamos sobre o que aconteceu na escola. (We spoke about what happened at school.)
4. Falamos sobre o assunto com toda a calma. (We spoke about the subject with all the calmness.)
5. Nós falamos sempre com educação. (We always speak with politeness.)