This is the description of the bug which was opened a long while ago, and that bug has not been resolved as of yet. This thread should be updated when that happens.
Unfortunately, no, because when you're working with a component, you are within a View. Views have absolutely no idea they will be used as a "Page", because there is every possibility that they will not be. Essentially, the View you are within knows ONLY about View properties, which include its children and any of their properties.
Not entirely true - assuming these Views will all be opening the same Docked View; you could easily make a small View which contained ONLY the button you're looking to use for the action, and then each View would utilize an Embedded View, which supplies a path to the View which contains your button. Now you've configured the Action in one View only one time, and you have Embedded Views in each of your Views which point at that View.