Self-employment is when one works for themselves for a client or for a contractually agreed upon fee for a specific service. There is no entitlement for wage continuation in the case of illness or vacation.
Typically, no Social Security Insurance obligation exists with exceptions of the pension insurance for certain services (see below) or for health insurance when the service is no longer part-time.
Pension Insurance obligation
According to the "Sozialgesetzbuch VI", certain self-employment occupations are obligated to pay a contribution to the pension insurance; e.g. teachers, educators, and caregivers, who do not employ others or self-employed persons who only has one client without an employer.
This insurance obligation also applies to part-time employment. The Pension Insurance obligation comes into effect once the income limits of part-time / low-income employment is exceeded.
A student is exempt from the pension insurance obligation during their studies at a higher education institution for the duration of a required "Praktikum" (professional development/internship).
Self-employed persons are also obligated to pay health insurance. Those who are under Family Insurance and have an income of more then EUR 450 a month are no longer qualified for the Family Insurance and are then required to pay the regular Student Health Insurance.
If the requirements for the Student Health Insurance are not met or are not provided (e.g. Income limit or working hours exceeded) then a voluntary insurance must be taken out.
For voluntary-insured-self-employed persons, a specific minimum income limit will determine the amount of the insurance fee. A minimum income limit exists also for part-time-self-employed (maximum of 18 hrs/wk) persons. More information can be found at the Bundesministerium für Gesundheit.
Self-employed persons are obligated to pay taxes. The Finanzamt can answer any questions about taxes for self-employed persons. There is a difference between the freelance and the commercially-self employed person. The "Ordnungsamt" or "Gewerberamt" can answer any questions about taxes for commercially-self-employed persons.