I believe we should be able to travel to Spain without a Schengen visa as NZL is on the proper list.
Some information implies that there is a right to refuse entry without an onward ticket. Being that we will be driving/on the ferry is this likely to be an issue?
No. In fact, there is no strict requirement for a return ticket, but even if there were, it would not apply to you.
What I am unclear on is the requirement for a residence card and when this should be applied for. Am I correct in saying that we can apply for this once in Spain and once granted this will effectively grant residency beyond the original 90 days?
Yes, you can (and must) apply for the residence card in Spain, but no, the residence card does not grant a right of residence beyond 90 days. That is why it's called a residence card instead of a residence permit. Under EU law, the card serves only as evidence of your family member's right to accompany you in Spain, which derives intrinsically from three facts: that she is your family member, that you are in Spain, and that you are an EU citizen.
Because of this, the penalties for failing to obtain the residence card are limited. They must be proportional to the penalties levied on Spanish citizens for failing to comply with identification requirements, and, in particular, they may not extend to removal or refusal of entry.
Because you are dependent on the "durable relationship" provision, however, the derivative right of residence does depend on "due attestation" of your relationship, so unless you marry or register your partnership before moving to Spain, you would indeed be well advised to apply before the 90-day period expires.
I am also unclear as to what documentation is required for unmarried partners. We have been in a long-term relationship and are engaged. However most of the sites I have seen suggest we need to supply a marriage certificate, which we don't have yet.
You don't need a marriage certificate. The definition of "family member" includes registered civil partners, and the rights also extend to "the partner with whom the Union citizen has a durable relationship, duly attested."
For her UK visa, we had to supply evidence of our relationship (essentially just letters to the same address). Is this sort of proof sufficient in Spain? If so, would every document need to be a certified translation even though the content is not relevant?
I don't know about this, I'm afraid. The criteria for "durable relationship" and "duly attested" are determined by individual member states, so your experience in the UK is not directly indicative of the Spanish requirements.
This is all specified in Directive 2004/38/EC. The effects of Brexit on the rights of British citizens and their family members living in other EU countries is uncertain as of January 2018.