Could we use "quand" or "que" instead of "où" here?
No. Quand is not a relative adverb. You use où for space and time.
In English the when is not required
Why not. It is the season when i won all my games?
C'est la saison où je gagnais tous mes matchs. I think this would have been a better sentence. Indeed that has been the way I have heard it said.
Why isn't it 'c'était'?
Why not 'that's the season where I won all my games' - I would say it that way in English naturally