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

Yes.

The word "querem" is identical in spelling, grammar, and meaning in both Brazilian and Continental Portuguese. The only difference is pronunciation. In Brazilian Portuguese, the vowels are typically more open and clearly articulated. In Continental Portuguese, unstressed vowels are often reduced or "swallowed," which can make the "e" in "querem" sound much shorter or almost silent, resulting in a more clipped sound.

Brazilian Portuguese Examples

1. Eles querem comer um lanche. (They want to eat a snack.)
2. Eles querem o novo celular. (They want the new cell phone.)
3. Eles querem pegar o ônibus. (They want to catch the bus.)
4. Eles querem ver o cachorro. (They want to see the dog.)
5. Eles querem comprar um trem de brinquedo. (They want to buy a toy train.)

Continental Portuguese Examples

1. Eles querem comer um lanche. (They want to eat a snack.)
2. Eles querem o novo telemóvel. (They want the new mobile phone.)
3. Eles querem apanhar o autocarro. (They want to catch the bus.)
4. Eles querem ver o cão. (They want to see the dog.)
5. Eles querem comprar um comboio de brinquedo. (They want to buy a toy train.)