"Is this newspaper independent?"
Translation:Is deze krant onafhankelijk?
Yes. Onafhankelijk (literaly) means they do not depend on anything or anyone. Zelfstandig means operating on their own. So in quite a lot of contexts they are synonyms. But in the context of a newspaper (and other press) onafhankelijk is used if their reporting is not influenced by the government, zelfstandig is used if they are not part of e.g. a big media concern, but run their own business.