Questions about cleft sentence

Do you use which or when in cleft sentences? If no, is there any grammar rule about this

For example,

It's money that we want. or It's money which we want.

It was today that I saw him. or It was today when I saw him.

I don’t think “which” works in your first example, as “money” is too generic. For me, “which” would only work when you are talking about some specific amount/entity of money, as opposed to referring to just “wanting money”, as in, “I work because I want money.”

Both are fine in your second example, but again I would go with “that” here. “When” is a somewhat “heavier”/more specific word, and so I wouldn’t use it unless it was necessary/required for the sake of clarity.