This is great feedback, thanks so much! I've created issues for your requests so we can track them: https://github.com/18F/checklistomania/issues. They all seem like they would add a lot of value. It is our hope that others in government and the public use this code, so we will do our best to deliver in a timely fashion.
Lead dev here - Yes, it supports that. It supports any task which can be expressed in the syntax "complete this [X] days after this [list of items] is done, where X can be positive, negative, or zero, and [list of items] could include just the special first task "dayZero" which sets the base date for the checklist or any other combination of tasks.