university in nz is relatively cheap and student loans are easy to get (an arts degree isn't much more than $20000, although a medical degree is $100k plus)most doing top flight degrees do a stint overseas to gain experience and earn more to pain off their student loans before returning home. Aussie is the same pretty much.
Sports stars can get school scholarships, but so can gifted kids. At college level as far as I'm aware there isn't anything -the focus is on academia not sports.
Players come up through provincial teams and I guess universities have nothing to do with selection.

Just a quick check of the scholarships page for NZ unis shows no sporting scholarships other than for support staff ie: coaches and physios'and most are no more than $5000.00 total. There aren't any free rides unless you have extreme hardship and even then I don't think so