Don’t laugh!
Why shouldn’t I?
Why didn't you confess your fault?
Why should I have?
These are examples from a grammar book on modals written by a Russian linguist. Examples she produces include sentences in present tense only, though the exercises given below include past tenses as well.
My Question is: should i use "have" to construct an equivalent of sentence №1 but in past tense. to be more precise - why should i have confessed?
In the first situation, the first speaker is giving some advice The second speaker is responding with a rhetorical question. The second speaker isn't really asking for a reason. He is saying "There is no reason for me not to laugh."
The second speaker is responding to a question about a past event. There is no way that they can change the past. It would be possible to use a past modal like this, but far more likely would be to answer the question.
The second speaker might answer the question but change the tense. If the reason for not confessing continues to the present it is more likely that the answer will be present tense:
Why didn't you confess your fault?
Why should I? I've done nothing wrong.
or actually answer with an explanation of the past:
If I'd confessed, I would've got into trouble.
I don't think it is useful to think of these as grammar manipulations (like changing active to passive voice) but as conversational contexts.
It might be worth noting that "confess your fault" sounds like a 1930s private school teacher, and is not the sort of thing you'd expect people to say nowadays.
The second sentence tense is used correctly. should is the past tense of shall, and you use it as you did there.
