1. Wordpress is probably better if you really want a platform to build something very custom off of, so in that sense it would be an alternative to a Django/Rails/Node solution. The downside is that it's a lot of work to both build and maintain, worrying about scaling, ongoing security patches and maintenance, etc.
2. One, Weebly is a much more intuitive, easy to use platform, two, we have a powerful ecommerce platform built-in (Wix doesn't have this), three, we have iOS and Android apps to create or manage everything from (no one else has that), four, we have a deep developer ecosystem (over 200 third party apps and integrations, the most of any platform), and five, the website, ecommerce, and email marketing is deeply integrated, others are more a collection of pieces.
3. Yes! There are a ton of APIs to build into Weebly, check it out here: http://dev.weebly.com/. You can also just copy and paste any code you want into your site with the embed code element. And if you're just looking to showcase code on your site, check this out: https://www.weebly.com/app-center/code-block?ref=ac-collecti...