When creating INotification instance with NotificationBuilder (via CreateNotification), you can set iOS properties with SetIosProperties and android properties with SetAndroidProperties methods.
You can make use of Tag property while setting the android specific properties when creating the notification.
Yes. Just enable "Allow Notification Display when Foreground" property in Settings under Android section.
It's possible to configure the payload keys of your choice in the plugin. Go to settings and set the payload keys as per your server setup.