Unless you have some on line backup service with Norton, then yes you should cancel. Why Norton would need to connect anywhere to uninstall their security tools? Are you sure you read all the relevant info about the specific removal utility you downloaded? Is it the “correct” removal utility?

It seems to me that you are not so sure what exactly you have in that system you bought. Maybe you have some (already) paid product from Norton installed and you are not taking advantage from it?

Any idea if you have some backup with Norton?

Do you have any progress with the potential malware issue (that should be still your first priority)?