1) no problem with that
2) you can count them, but the real question is will the NZ instructor will actually teach you anything or is he just taking you for a joyride? It is also up to your home ATO to assess you whether you've actually gained any skills or some bits and pieces need to be repeated/fixed etc. With all likelihood you will not finish your course within 45 hour minimum, so I wouldn't worry too much about it, just go and have fun!
3) to elaborate on gordonquinns answer above: to start a modular CPL course you need 150 hours total time, the regulations don't specify how many of these should be dual or PIC.. in this regard I can't see how any aul 20 extra dual hours will hurt you. However to FINISH a CPL you will need 200 hours of which 100 hours should be PIC. Because your CPL modular course is pretty much dual instruction with no to very little solo time, you should realistically walk into your training with 100 PIC hours already in your logbook.
So ultimately if your goal is to achieve your CPL with minimum hours, any extra bimble you do with any extra FI outside your training program will probably hurt your chances. However, you should also aim to enjoy your training and if I was in NZ for a while I would definitely do it, not only for fun, but for staying current as well