Does eValid have an programmable interface -- The EPI is very powerful and connects directly to the browser so you can "drive" your web page as you wish your tests to do.
Changes or deletions of content in the DOM -- Yes, dynamic DOM updates can complicated otherwise straightforward testing, but eValid has the resources to overcome the problem.
Is eValid considered a no code solution -- If a "no code" means you don't HAVE to code, then eValid fits the description. But you can code if you want to (with the EPI option).