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

Yes

The difference between the two dialects is strictly phonetic. In Brazilian Portuguese, vowels are generally more "open" and clearly articulated, so the "a" at the end of "estuda" is pronounced distinctly. In Continental Portuguese, unstressed vowels are often "reduced" or "swallowed," meaning the final "a" may sound much shorter, more closed, or even nearly silent depending on the speaker's regional accent. The spelling, grammar, and literal meaning of the word remain identical.

Brazilian Portuguese

1. Ele estuda muito para a prova. (He studies a lot for the test.)
2. Minha irmã estuda medicina na faculdade. (My sister studies medicine at college.)
3. O menino estuda todo dia. (The boy studies every day.)
4. Ela estuda inglês sozinha. (She studies English on her own.)
5. Ele estuda bastante para o vestibular. (He studies a lot for the college entrance exam.)

Continental Portuguese

1. Ele estuda muito para o exame. (He studies a lot for the exam.)
2. A minha irmã estuda medicina na universidade. (My sister studies medicine at the university.)
3. O rapaz estuda todos os dias. (The boy studies every day.)
4. Ela estuda inglês sozinha. (She studies English on her own.)
5. Ele estuda imenso para o exame de admissão. (He studies immensely/a lot for the entrance exam.)