Welcome to AN as a participant :)
I live in Melbourne, and work with adults, so I can't help with most of your questions. Every public hospital I know has rotating shifts, though many nurses have a degree of flexibility with their rosters. I, for example, work nights at least nine months a year, and I've worked with nurses who hadn't done a day shift in several years. A lot of this depends on the needs and putlook of the NUM, of course, but I haven't ever seen an advertised position for one shift only. Also, I believe NSW, like Victoira, predominantly works an 8:8:10 roster - for the most part 12/24 shifts are limited to ICU and psych.
You seem surprised that a Masters as an international student is of comparable cost to one at home, though I'm not sure why. Full-time nurses in Victoria, and I imagine it's the same or similar in NSW, are entitled to paid leave for post-graduate study relevant to their current role - here that's 4 hours/week for 26 weeks a year, plus up to five days annually for study, conferences and exams. The more usual issue is people on student visas working, so I'd be surprised if this was a visa issue, but it's not a bad idea to check with the Immigration Department.
NSW recently one nurse: patient ratios, so that's soemthing that won't be too different :) Good luck with your move - I hope it goes smoothly, and that other members are able to give you more specific adice about PICU and NICU units up north.