Can I install Mint on one domain/server and use it to track hits on another?
Yes. A license should be purchased for the external domain Mint will be installed on. A license should be purchased for each instance of Mint installed to track an individual domain (Some browsers automatically ignore cookies set by an external domain as a privacy consideration. Mint will still function but in some cases identifying unique visitors may not be possible on external domains.)
http://thedomainhostingmint.com/mint/?js), not the default relative url (eg.