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

Yes

The word "devagar" is identical in meaning, spelling, and grammatical function in both Brazilian and Continental Portuguese. The only differences lie in pronunciation:

• Vowels: In Brazil, the vowels tend to be more open and the rhythm is more melodic (syllable-timed). In Portugal, the vowels are often more "closed" or reduced, making the word sound more clipped.
• The "r" sound: Depending on the region of Brazil, the final "r" might be aspirated (like an "h") or retroflex (the "caipira" R). In Portugal, the "r" is typically more alveolar (tapped or slightly trilled).

Brazilian Portuguese Examples

1. Dirija devagar, a estrada está perigosa. (Drive slowly, the road is dangerous.)
2. Eu gosto de caminhar devagar pelo parque. (I like to walk slowly through the park.)
3. Fala mais devagar, por favor, eu não entendi. (Speak more slowly, please, I didn't understand.)
4. O processo vai ser devagar no começo. (The process will be slow at the beginning.)
5. Vamos devagar para não cansar. (Let's go slowly so we don't get tired.)

Continental Portuguese Examples

1. Conduz devagar, a estrada está perigosa. (Drive slowly, the road is dangerous.)
2. Gosto de caminhar devagar pelo parque. (I like to walk slowly through the park.)
3. Fala mais devagar, por favor, eu não percebi. (Speak more slowly, please, I didn't understand.)
4. O processo vai ser devagar no início. (The process will be slow at the beginning.)
5. Vamos devagar para não nos cansarmos. (Let's go slowly so we don't get tired.)