No, running the previous version of XML::SAX is unlikely to cause a problem although parsing of XML will be very slow.

The error you got when trying to install XML::Parser was simply because you don't have the expat header files installed. Typically the expat library would be in a package called something like libexpat and the headers would be in a package called libexpat-dev. You'd need both to build XML::Parser.

On Linux servers, it's generally easier to install the OS packages for CPAN modules if they're available.