is OPE able to produce different cyphertext for same plaintext? Given a plaintext p, is OPE (Boldyreva et al.) able to produce n different cyphertext c1...cn for the n occurrences of p?
If not, there exists an order-preserving encryption scheme able to do that?
Boldyreva et al.'s scheme is not randomized. However, there is a folklore way to "randomize" it by choosing randomly from the range gap in the last recursive step of the algorithm. It's not clear what security improvement this buys you, though, since it only really randomizes the last few bits of the ciphertext. 

There are schemes meeting a randomized version of Boldyreva et al.'s IND-OCPA definition (q.v. Kerschbaum, CCS'15) but they require large client storage.