Integration with TST: It looks possible, they provide an API this add-on can use to do this. I'll have to consider whether integrating with other add-ons like this is something I want to support, but at the moment I'm leaning towards not. I've created issue #40 on my github repo to track this request.

Dragging to edges: This is a Firefox bug, I'll have to refer you to their Bugzilla for this. I did not find an existing bug when I did a quick search so you might want to create one.