It's not necessarily an SEO problem (as long as you don't redirect all 404s to your homepage at least. I've seen that be an issue in the past.)

However, use it as an opportunity.  Make the 404 a sales page if you have that many.  It's a lander now for "the product you were searching for is out of stock - here are the search results on our site for similar products" etc.  You can turn it into something productive to have that many 404s.

From WMT, mark them as fixed and then anytime one pops up, find out what is linking to the product and try to remove that link.  You don't want to be linking to 404s internally if you can help it (bad user experience = Google's nightmare) so having 1000s of 404s isn't bad but try to break any internal links to them.  (Xenu can help as well if you don't feel like waiting for WMT.)

Not bad for the homepage as far as I know - but it does seem to be bad for the internal pages you link to as any 'juice' that is passed is diluted by the amount of links you have. Internal linking & navigation is good, but don't overdo it with spammy footer links that all point to keyword-rich anchors back to your site, especially repeated ones.

Duplicate the content onto nz.example.com and then use the hreflang tags.

You haven't blocked http but you've implemented https.  So you're allowing Google to crawl both versions of each page. And yes, you should probably block the non-https.

I'm pretty sure meta language is the only thing Bing recognizes for language at this point.

http://returnonnow.com/2012/06/international-seo-hreflang-tag/

For any other search engines, you need to employ the Meta Language Tag. There are two ways to set up the syntax on this tag:

Or the alternative syntax would be:

If the site is only targeting a language, the latter would suffice. However, if you are targeting to language and country (e.g. Spanish for Spain vs. Mexico), use the first option.