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

Yes

The word ficou is identical in spelling, grammar, and fundamental meaning across both Brazilian and Continental Portuguese. In both dialects, it is the third-person singular preterite (past tense) of the verb ficar, and it is used to express that someone or something "stayed," "remained," or "became" (a change of state). The only significant difference lies in pronunciation; Brazilian Portuguese tends to have a more open, musical rhythm with different vowel reduction patterns, whereas Continental Portuguese features more closed vowels and a more stress-timed, "staccato" cadence.

Brazilian Portuguese Examples

1. Ele ficou muito feliz com o presente. (He became very happy with the gift.)
2. O ônibus ficou parado na avenida. (The bus stayed stopped on the avenue.)
3. O bolo ficou uma delícia. (The cake turned out delicious.)
4. Ficou um pouco de suco na garrafa. (A little bit of juice was left in the bottle.)
5. Ela ficou estudando até tarde. (She stayed studying until late.)

Continental Portuguese Examples

1. Ele ficou muito contente com o presente. (He became very happy with the gift.) Note: "Contente" is often preferred in Portugal for this context.
2. O autocarro ficou parado na avenida. (The bus stayed stopped on the avenue.) Note: "Autocarro" is used instead of "ônibus".
3. O bolo ficou uma delícia. (The cake turned out delicious.)
4. Ficou um pouco de sumo na garrafa. (A little bit of juice was left in the bottle.) Note: "Sumo" is used instead of "suco".
5. Ela ficou a estudar até tarde. (She stayed studying until late.) Note: The "a + infinitive" construction is the natural way to express ongoing action in Portugal, whereas Brazil uses the gerund ("estudando").