Security Level Estimate when Cascading/Compositing Ciphers?
First question

It depends upon the scheme.  It also depends upon what kind of composition you are talking about.  Triple-DES uses multiple encryption.  That's one kind of composition.  The approaches you talk about in your third and fourth questions are a different sort of composition.  They will have different security properties.

Second question

Yes.  If the operation forms a group, then using multiple encryption does not add security.

Third question

This provides only 128-129 bits of security, but not for the reasons you expected.  The reason is Diffie-Hellman with a 3072 bit modulus provides only about 128 bits of security; one can break Diffie-Hellman with a 3072 bit modulus using something like $2^{128}$ work (very roughly).  So, one can break two Diffie-Hellman exchanges using $2^{129}$ work (very roughly).  In other words, this does not add security.

This is not a practical weakness in practice, because in practice 128 bits of security is more than enough; no one is going to be able to perform a computation that requires $2^{128}$ work (not in my lifetime).  That said, this is a certificational weakness in the protocol, and no one would consider this to be good protocol design; it is rather crummy protocol design.

Fourth question

Same answer.



Final note

This is kind of silly.  Why don't you tell us the real problem you really have?  It sounds like your question is heading in the direction of crummy protocol designs.  Maybe if you tell us the real problem, we can help you find a better solution to the problem.