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

Yes

The word "mexer" is identical in both Brazilian and European Portuguese in terms of meaning, spelling, and grammar. The only differences are phonetic. In Brazilian Portuguese, the "x" is typically pronounced as a "sh" sound (/ʃ/), and the vowels are generally more open. In European Portuguese, the pronunciation is more closed, and the articulation of the "x" is often more subtle or slightly different depending on the regional dialect.

Brazilian Portuguese Examples:

1. Não mexa no meu celular. (Don't touch my cell phone.)
2. Você precisa mexer bem o açúcar. (You need to stir the sugar well.)
3. Eu adoro mexer em antiguidades. (I love tinkering with antiques.)
4. Ele não consegue parar de mexer as pernas. (He can't stop moving his legs.)
5. Não mexa com ele, ele está bravo. (Don't mess with him, he is angry.)

European Portuguese Examples:

1. Não mexas no meu telemóvel. (Don't touch my mobile phone.)
2. Precisas de mexer bem o açúcar. (You need to stir the sugar well.)
3. Eu adoro mexer em antiguidades. (I love tinkering with antiques.)
4. Ele não consegue parar de mexer as pernas. (He can't stop moving his legs.)
5. Não mexas com ele, ele está zangado. (Don't mess with him, he is angry.)