Sorry, These question-mark were my typos error. (Edited)The sentences are all written as statements, but the question-mark indicates that they are meant to be questions. Do you mean them to be questions?
(When we write, we cannot show the intonation that might be used when speaking - and that would let us know whether the sentences are interrogative.)
Okay, Thank you Sir
- He has not played cricket or hockey = he didn't play cricket, he didn't play hockey. This is the most normal.
- He has not played cricket and hockey = he didn't play the cricket+hockey combination that the school offered or that you just alleged. This would be unusual.
- He has played neither cricket nor hockey = same as no.1 but more formal.