I was able to register to your site without issue, however I too got the 404 error when clicking on the link. When I examine the URL for the link I think that I can spot the issue, it looks like the URL you have for the user confirmation page is actually going to
The problem is that the TLD is not defined, so when I click on this link I'm taken to this page:
This is when the 404 occurs, to fix this you should make sure to put in the .co.nz into the URL for your site. This should get the user directed to the correct page. When I manually update the link to go to .co.nz it takes me to the correct page where my email address is verified.
Once my email was verified I was able to login to the site without issue.
In regards to the email receipt it looks like things going through ok on the site, could you post your confirm page in a zip archive to this thread so that it can be looked at more closely. If it contains any sensitive details don't post it and I can open a ticket for you to post.