of course you can refuse service, if you dont think the ID is them, then you dont serve them espescially when you say it's "obvious" they are using somebody elses.
yes it is illegal, and yes u can refuse service.
as an aside, fuck, i wish they would integrate a few services of the various help desks, or at least COMMUNICATE with each other. EFTPOS didnt balance monday morning, we couldnt figure out the problem at first, so just shortbanked to 23 after calling IT helpdesk, then calling GFS. So, finally, i work out the problem is from a few days earlier when a few transactions somehow got sent to the bank a day late. so me, being a good boy decides to try work out what happened and fix it
-call GFS, they cant find the transactions, they tell me to Manual Export the pinpad
-do this, doesnt work, call IT help desk
-IT help desk tells me to call SSS (because they will have a better idea of what has happened, apparantly), then call back GFS