Is "arbetare" only applicable to "workers" and not "employees"? If so, is there another word for "employees"?
Yes, arbetare and workers are pretty much the same, and employees and anställda are a very good match with each other too.
While that is true, isn't the question being asked here really about employees? Or is it common in Sweden to just have workers who are not employees? Because that is a not a common question for English. I would imagine that the meaning is what us important here, so Employees should be allowed as an answer.
Workers are a special kind of employee. The number of employees in a company might be much higher than the number of workers...
just to clarify: when you end with "do you have?" in swedish it is "har du" or "har ni"?