What foreign currency exchange rate is applied ?
The rate applied is "Standard Rate". Different geographies / Banks call it by different names, Card Rate / Sheet Rate / TT Rates / etc. Essentially depending on the currency pair and market the Treasury function at Bank determines a standard rate that is to be used for the day. These have sufficient margins to cater to normal fluctuations during the day. Some Banks specifically create a ATM Rate that has higher margin to offset the loss due to fraudulent withdrawal.
There are other preferential rates and negotiated rates available for large corporates for larger transaction values.
Is there a universal exchange rate or do the banks use their "own" ?
Every Bank uses its own rate. However it has to be competitive and generally do not create an opportunity for gain. i.e. if You convert Euro to NZD at one bank and then take the NZD and convert back to Euro, you loose money. At certain times there is a window when you do large hops between EURO/USD/GBP/YEN/AUD/ etc. However this opportunity is not present for Standard rates.
Does the price fluctuate during the same day ?
See point 1. Generally "Standard Rates" do not fluctuate on stable pair of currencies. So for Euro/NZD the Standard Rates should be same. However if you take say Indonesia Rupaiya / USD or some other weaker currency, the Standard Rates may be revised by Treasury couple of time a day. If the pair is very unstable, generally Banks suspend trading. In case where it is not able to say someone withdrawing cash at ATM; the rates for such currencies are very very bad and would have huge margins.