After 'make install', can I 'rm *' to remove the tarball and all its extracted files?

Yes. After make install has completed successfully it's safe to delete the installation files. If you'd like to be sure the module installed successfully, run a script that uses it, or just something like perl -MModule::Name -le 'print $Module::Name::VERSION'. (The only exception might be if you've done some customization in the source directory that you want to keep around.)