(a) Yes. Although it is not expressly agreed, it would be a term of this contract that Peter carry out the work with due care and skill. On the known facts, Peter appears to have breached this term.

(b) No. Unless it was expressly agreed, it would not be a term of the contract that Peter carry out the work with due care and skill. In the absence of such a term, there is no breach of contract by Peter.

(c) No. Peter only promised that he was qualified to do the job, and even qualified persons can make mistakes. There is no breach of contract in these circumstances.