1. Oddly enough, I don �t use the contraction mustn �t very often with the perfect tense, although "can �t have _____" sounds fine to me. With must not have, I come to a conclusion that something didn �t happen. Example: "There is a big puddle of melted ice cream on my counter. I must not have put it back in the freezer." With can �t have, I know something didn �t happen because of contradictory evidence. Example: "I can �t have bounced a check! I deposited my paycheck last week!"
2. He should be tired. That implies that he did something after which it is reasonable to believe that he is tired. Example: "He should be tired. He ran a marathon today."
3. Should have done is always in the past, either for an unfulfilled obligation or for an action that would have been better than the action that was taken. Unfulfilled obligation: "She should have gone to work today, but she had the flu." Better action:" He should have gone to bed earlier last night. Now he can hardly keep his eyes open during the meeting."
4. We do still use ought to (often pronounced "oughta"), but not as much as should. At least in American English, we rarely use needn �t. We use don �t/doesn �t need to much more.
5. I would say we use couldn �t have done even more than can �t have done. It �s perfectly okay.
That �s my take on it as an American English speaker. I hope it was helpful.
.Also as I �m not a native speaker , I couldnt give satisfying answers. If sb especially native one helps me, I �ll be grateful.
but I hope this links can help you 
