In order to refer a patient you need to attempt to send them the ward when it is full. You will get a pop up asking to refer them to a friend. A list of friends will pop up and after they accept the request you get the achievement.
For the second one, I'm stuck on that one too. I also send energy gifts every day and have made no progress. I think it might be a bug.
I did not find the right solution from the internet.