Is it possible to use one framework written in one Parrot (LLVM) language in any other Parrot (LLVM) language? (Like usage of .NET Framework from any CLR language)...
Parrot and LLVM are two different things made by two different organizations.
Parrot is a VM, and LLVM is a VM that can also compile statically.
Edit
Assuming the comments to my answer are correct:
http://en.wikipedia.org/wiki/Comparison_of_application_virtual_machines