Just an update on this question, Agileware have developed the following for Caldera Forms:
EWAY payment gateway integration for Caldera Forms using EWAY Rapid 3.0 API
CiviCRM recurring payments for memberships and donations using Caldera Forms
Ability to view and update stored credit cards using Caldera Forms
This work will / is and be publicised in a ...
Not at present - I've investigated this myself in the past. You can find a complete list of actions in their repository (though of course other extensions add actions).
I considered writing the action but it turned out to be complex. A rule that adds everyone to a pre-determined event is easy enough - but creating a UI that could handle actions like "Add ...