How to paraphrase It is "possible" and "impossible" to clauses into that clauses?

Please help me to recover from my splitting headaches due to the usages of “possible” and “impossible”, especially in case of “ how to change it into that clause or when to use ”should“ in that clause.” Please teach me about their grammaticality. Thank you in advance, native grammarians!!!



1. He may be rich.=It is possible that he is rich.

2. He cannot be rich.-Which is correct of the following two? or is neither of the following grammatically correct?
=It is impossible that he is rich???? or
=It is impossible that he should be rich????

3. He cannot have solve the problem. -Which is correct of the following two and has the same meaning? or is neither of the following grammatically correct?
=It is impossible that he solved the problem.???? or
=It is impossible that he should have solved the problem????

4. It is impossible for me to solve the problem.
Which is grammatically correct and has the same meaning? or is neither of the following grammatically correct?
=It is impossible that I solve the problem?????
=It is impossible that I should solve the problem????

5. It is possible for me to solve the problem.
Which is grammatically correct and has the same meaning? or is neither of the following grammatically correct?
It is possible that I solve the problem???
It is possible that I should solve the problem???