Prevent taking action on posts that aren't editable in the current context.
Update the post statuses required by `notify_central_of_new_requests()`.

Custom statuses were introduced in e2158513c9289fe4dc201627f136232776d8fe0f and this should have been updated at that time.
Remove the Status column from the Payment Requests screen.

Each post's status was added to the Title cell in ddc221d1b1b7c9e9dd0a5704ad240349b7e5a45c, which made the UI mode consistent with Core, and the extra column no longer necessary.
Move `notify_central_of_new_requests()` to be after `save_payment()` in source.

This makes its location consistent with how the hook callbacks appear in `__construct()`.