@Stan and @jwpat have dealt with your first question in their comments. I will attempt to answer your second question:
what do you call a freelancer working at home?
People who work at home are usually referred to as homeworkers or teleworkers or telecommuters. These words describe a working arrangement and not the employment or contractual status of the worker.
There is no word to distinguish between a freelancer who works at home and other people who work at home (for example, permanent employees, part-time employees, and temporary employees).
I think you may have misinterpreted the definition. According to The Free Dictionary by Farlex, an e-lancer is
An independent contractor who performs his/her duties predominantly or exclusively online.
The reference to "at home" is given as an example.
I agree with the other comments that homepreneur is ugly and hokey, but in any case I don't think it is a good description of someone who does freelance work. A freelancer does well-defined assignments at a fixed hourly rate. The revenue potential is limited by the number of hours the freelancer can work, but the risk is also limited. An entrepreneur has greater revenue potential but also takes on a bigger risk. A freelancer could become an entrepreneur by taking on more work and hiring more people to deliver it. In all of this, whether the work is done from somebody's home or somewhere else is irrelevant.