The world is mobile today. Most people are searching on Google using a mobile device. The desktop version of a site might be difficult to view and use on a mobile device. As a result, having a mobile ready site is critical to your online presence. In fact, starting in late 2016, Google has begun experiments to primarily use the mobile version of a site's content42 for ranking, parsing structured data, and generating snippets.
Hey Ted, thanks for the great questions! The peak times refer to your particular time zone, if you are targeting an audience that resides in the same zone as you. You can also use tools to find out when most of your audience is online. For example, Facebook has this built into their Page Insights. For Twitter, you can use https://followerwonk.com/. Many social posting tools also offer this functionality.