Hi Nicky,
Have you read the
Guide for Returning Resident's Visas ? If you scroll down to page 6 it gives you some idea of the conditions that apply to getting one and keeping one.
Basically, your PR will be activated once you enter NZ to stay. There will already be a RRV in your passport along with your PR. During each of the next 2 years you have to show your commitment to NZ by remaining in the country for a minimum of 184 days (just over 6 months). In your daughter's case, when she leaves NZ to go back to the UK her PR will be cancelled. The RRV is in her passport to ensure that she can get back into NZ when she wants to come again and a new PR will be issued upon re-entry. This way they can keep tabs on how long she stays in NZ and if, at the end of the 2-year qualifying period, she hasn't 'proved her commitment' by living in NZ for 184 days in each year, she probably won't be able to apply for an Indefinite RRV. There are other rules and regulations, ifs and buts, which you can read about in the above link.
With regard to the English language thingy in the EOI form, not having had sight of the form, I can't say exactly what goes where. Suffice to say that, as a national of the UK where English is your first language, you just need to put the minimum that qualifies your statement that you are a native English speaker. Having said that English is your first language should be enough, I'd have thought. Reading the form again, does it actually say that you need to tick any of those boxes? It could be only for those for whom English isn't their first language. I'm sure some of the others will put you straight on this better than I can.