You are partially correct. Sign in with friends account. Set as home. He does the same. You dont set your home xbox as you again, leave it alone after you set it has your friends. "Do I need to fully download or just start the download" I have no clue what you are trying to get at with this question but you just need to download the game.
Read the article I provided for more information and good luck. Btw this question gets asked daily here and there is hundreds of posts here, you would have found your answer quicker if you would have searched this subreddit instead of making a post.