If you can get them out of the jar, I would suggest a hammer.
Put them in a plastic bag and whack them with the hammer.
You might be able to use a knife (carefully) to pry them apart depending on much they are stuck together.
That's a processed cheese product. It may be allowed to be called cheese in some places, but that's a matter of product labelling regulations where you happen to be.
The melting is a different issue. I'd expect that product to melt, though possibly not if it has the texture of parmesan - parmesan doesn't really melt on its own though it melts into sauces. ...