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

Yes

The word "pedi" is the first-person singular form of the verb pedir (to ask/request/order) in the pretérito perfeito do indicativo (simple past). The meaning, spelling, and grammatical category are identical in both Brazilian and Continental Portuguese. The only differences lie in the pronunciation of the vowel "e" (which may vary between an open [ɛ] and a closed [e] sound depending on the region) and the syntactic construction that typically follows the word (the infinitive construction in Brazil versus the subjunctive construction in Portugal).

Brazilian Portuguese Examples

1. Eu pedi uma pizza ontem à noite. (I ordered a pizza last night.)
2. Eu pedi para ele me ligar mais tarde. (I asked him to call me later.)
3. Eu pedi desculpas pelo que eu disse. (I apologized for what I said.)
4. Eu pedi um suco de laranja. (I ordered an orange juice.)
5. Eu pedi para a professora repetir a explicação. (I asked the teacher to repeat the explanation.)

Continental Portuguese Examples

1. Eu pedi uma pizza ontem à noite. (I ordered a pizza last night.)
2. Eu pedi que ele me ligasse mais tarde. (I asked that he call me later.)
3. Eu pedi desculpa pelo que eu disse. (I apologized for what I said.)
4. Eu pedi um sumo de laranja. (I ordered an orange juice.)
5. Eu pedi que a professora repetisse a explicação. (I asked that the teacher repeat the explanation.)