Can I keep 2 copies of the same doc synchronized in two different libraries so that if one gets updated the other does too?
With Sharepoint Designer you could create a workflow that is initiated when an item is modified. I know that with a 2010 workflow (also compatible with 2013, not sure about SPO) there is a copy to [document library] command. Which would do what you need.
Here is an existing post which deals with this subject. Here's another one for your research.
