Here is my question:

1. What is the Umbraco 7 prescribed method to add an Action to the "Default Permissions" list in UserTypes and then have it show up in the context menu for users who have that permission?

This is what I've got so far:

I created this class which gives me the Checkbox in Default Permissions:

public class TestNewPermission : IAction
{
    public char Letter
    {
        get { return '+';}
    }

    public bool ShowInNotifier
    {
        get{ return true;}
    }

    public string Alias
    {
        get{return "TestNewPermission";}
    }

    public bool CanBePermissionAssigned
    {
        get {return true;}
    }

    public string Icon
    {
        get { return umbraco.BusinessLogic.Actions.ActionNotify.Instance.Icon; }
    }

    public string JsFunctionName
    {
        get { return "LogToConsole();"; }
    }

    public string JsSource
    {
        get { return "function LogToConsole(){ Console.Log('Function From IAction was hit'); }"; }
    }
}

Then I hooked into the Tree Menu Rendering Event to show this action where users have the permission.

Example A:

 private void TreeControllerBase_MenuRendering(TreeControllerBase sender, MenuRenderingEventArgs e)
    {
        if (sender.TreeAlias == "content" && sender.Security.CurrentUser.UserType.Permissions.Contains("+"))
        {
            e.Menu.Items.Add(new MenuItem(new TestNewPermission(), "My Custom Action"));
        }
    }

I noted that the overload to use this IAction for MenuItem read:

public MenuItem(IAction legacyMenu, string name = "");

When I select "My Custom Action" from the Context Menu it doesn't run the javascript defined in the IAction class.

I also went a different route and built a MenuItem object and added it via the permission:

Example B:

   private void TreeControllerBase_MenuRendering(TreeControllerBase sender, MenuRenderingEventArgs e)
        {
            MenuItem myMenuItem = new MenuItem();
            myMenuItem.Name = "New Action Test";
            myMenuItem.Alias = "Test";
            myMenuItem.Icon = umbraco.BusinessLogic.Actions.ActionNotify.Instance.Icon;
            myMenuItem.SeperatorBefore = true;

            if (sender.TreeAlias == "content" && sender.Security.CurrentUser.UserType.Permissions.Contains("+"))
            {
                e.Menu.Items.Add(myMenuItem);
            }
        }

Even when using Method B, the solution still requires the new IAction class so that the to that the '+' permission can be assigned to the UserType. If Action is considered "legacy," why would it still be needed to accomplish this?