ECJ case C-68/89 Commission v Netherlands  makes clear that EU citizens are not required to answer border officials’ questions about the purpose and duration of their journey, nor about how much money they have for the journey.
Though this particular case concerned an EU citizen, the ruling applies equally to border officials, such as United Kingdom Border Agency ECOs, who issue the visas that enable free-movement of family members of EU citizens. If it is prohibited to require of the EU citizen, then border officials cannot bypass that prohibition by simply requiring that same information instead from their accompanying non-EU spouse.
Moreover, these questions are no more relevant for a family member then they are for an EU citizen. The conditional free movement rights of the non-EU family member derive directly from their relationship to the EU citizen (MRAX, paragraph 74). The visa is a formality to pre-validate the family relationship and facilitate the applicant’s travel arrangements.
The visa does not depend on assets the applicant has, or on what they plan to do during the trip.
Refusal to answer such not-material questions cannot justify curtailing the applicant’s right of free movement (see “Restrictions on freedom of movement”).
ECJ case C-459/99 MRAX v Etat Belge  is clear that what is required for entry of the family member who does not have a required visa is two things: proof of their family relationship (e.g. a marriage certificate) to the EU citizen and proof of their identity (e.g. a passport). There is no requirement outlined that the family member must answer non-material questions of the border official.
NOTE: This post was originally written as part of a complaint to the European Commission about UKBA (the British immigration agency) handling of EEA Family Permits, hence the references to the UK. But each EU member state must reflect ECJ court decisions in their national law and practice, and do so faithfully to the original decision. This case and European free movement law applies equally in each of the 27 member states!