For your manager class you should take a look at Singletons (Autoload), they are made almost exactly for that kind of job.
As for getting all nodes of a certain type, do you mean getting all nodes in a running scene?, if that's the case, and as is explained in the link provided, you can, in your Singleton script, get the parent node of the running scene with:
var current_scene = null
var root = get_tree().get_root()
current_scene = root.get_child(root.get_child_count() - 1)
and from there iterate through the children and check with
get_name() if is the node you are looking for.
hope that helps.