In this particular case the top action has the usual icon indicating that it’s a repeating action. The bottom action is weird. I’m guessing it used to be a clone of another repeating action which you transformed into a repeating action itself. This doesn’t usually happen. Basically the round arrow icon you are seeing in the bottom action indicates that it is an automatically created clone. more about how repeating items work with pictures
Yes, it’s not possible to re-order the Scheduled list - the order is automatic based on nearest scheduled dates.
The Contexts section contains the tags which start with “@”. Other than that, contexts are just tags.
Everdo doesn’t provide any special functionality for this. There were a few suggestions, but it’s still not clear what the functionality should be.
Move it to Next and the back to Waiting
You either view the full aggregated Next list, or open the specific project to see it’s own Next list.
Could be done at some point, but many other features are in the queue 
Yes, it’s on the list.