If a person is diagnosed with primary dystonia but there is no family history, does that mean it’s not genetic?

No. Typically the word "primary" in reference to dystonias is used to talk about genetically-associated dystonias. Not having a known family history of the disease does not necessarily mean it is not genetic. Some of the dystonias that are genetic are passed down through carriers which can make them relatively rare, even among families of carriers.
It depends. Dystonia is just a description of abnormal muscle tone. Dystonia can affect small muscles or separate limbs or total body. Some cases are progressive and severe while others are transient and resolve to normal. Ther are some forms associated with genetic and metabolic disorders. Many cases are primary without cause or genetic association.