This seems like a linking problem with Intel's Math Kernel Library. You have many questions, so I will try to address each one.
In general, when there is a linking problem, especially "cannot find -lfoo", check the search directories. These are options that are usually specified with -L such as "-L /path/to/libraries". In your case, the intel compilers should usually accept the "-lmkl" option which internally specifies the location to the libraries. This does not solve your problem, though.
Since you are usually PETSc, and you are getting this error, it means that you are trying to switch the compilers or BLAS/LAPACK library after building PETSc. This is not supported. So, yes, you will need to reconfigure and rebuild specifying the Intel compilers and MKL. See the installation help for more information.
There are many libraries that need to be linked so that you can use Intel's MKL. Intel even made a helpful page to build the command-line link option.