Newbie questions as I look to build a solution for Dynamics

I'm very excited to take an app that I have published on another CRM's app store, and build an equivalent for Dynamics! After doing a whole lot of research, I'm still left with a few questions, many of which are probably pretty easy for most of you folks to answer:

My solution will require custom entities, a custom UI, and custom logic. This leads me to some questions:

Housekeeping questions:

1. How do you test on older versions of Dynamics? Trial versions seem to be only 2016, so do I really have to buy a license for the older versions if I want to test my solution on them?
2. Are there any usage statistics on 2011, 2013, 2015, and 2016? If not, how do you generally decide how far back you need to support?

Technical question:

All JS examples that I've seen are just performing basic CRUD on entities. I'd like to write some more complex server-side logic and define a custom API endpoint which I can hit from the client (JS). When I hit this custom API endpoint, I'd like to execute some logic, have some things happen on the server side, and return the result to the client for display in the UI. It's quite a bit more involved than just the basic CRUD examples that I'm seeing. Is this possible, or is all business logic strictly confined to triggers, workflows, and client-side logic?