No. There is a minimum wage (8,50 Euro per hour) and it is illegal to pay less. No matter how much hours you work per week. Of course it is possible that an employer pays more than the minimum wage per hour. That always depends on your work contract.
Keep in mind that there is a huge difference between regular jobs and self-employed. When you are self-employed it can happen that your income is lower than the minimum wage. The amount of money that ends up on your bank account always depends on how much sales your business generates.
part-time jobs are good for people that want to study at the same time, that are parents or that have to go to integration classes. Usually you work 40 hours a week, but you have the right to ask your employer if you can do it in part-time. If you work part-time the workload reduces to an amount of time between 20 or 30 hours a week.
Can I work part-time and work as a freelancer at the same time?