Is part-time working online from home, legally correct for a person already employed in another company?
It is legal. However, many companies (like mine) have policies restricting work outside of the company, unless you disclose it and it is authorized. The main concern is that the position will take away from time you would spend working for your main company, or that you would use company resources to conduct business for another company. If your company has no policy on this, then there is no issue.