First off outlook should be able to connect to your Hotmail or Live Hotmail already you just have to configure it to do so. As for google that will require a third party to allow you to access gmail without having to go to google. I used outlook to read and delete and view my hotmail without any third party software. Once you set outlook for hotmail you have to go to the more settings and there should be where you can tell it to delete from hotmail when you delete from your local computer. I have read about a app that will allow you to access your gmail and delete emails without having to login into gmail but I don’t recall that program as of right now.