Hi Stacey! Thanks for your questions and for your interest in the game.

This article in our official website's FAQ will answer all of your questions regarding sickness and guide you on raising a healthy and happy family:

https://ldw.zendesk.com/hc/en-us/articles/209711313-Family-Health-Sicknesses-Cures

Additionally, the time of day won't adversely affect your game play, but if you do need to take a significant amount of time off from the game, there's a "Pause Game" option in the settings menu!