Hi there,
Personal liability insurance policies generally cover an individual or a family. The locations in which incidents occur are not the deciding factor. You can remain covered by your family's personal liability insurance for as long as your family's home continues to be your primary residence and you remain single and unemployed.
Part-time employment of 30% will not normally qualify you as an employed person, but the exact definition of "employed" can vary between insurance providers. A good first step is to have your parents either review their policy carefully or contact their insurance provider and explain the situation. If there is any doubt about coverage, consider getting your own personal liability insurance policy.
Household insurance generally covers a specific property. Unless you have optional coverage against simple theft away from home, only personal property kept in your primary residence is covered against theft. If you stay in shared housing or a boarding house, ask your host if their household insurance covers all members of the commune. You can learn more in our guide to insurance for shared housing.
Best regards from Moneyguru