Hi Jacci,
It looks like you’ve got some CSS issues that are messing with things. I see some custom CSS you’ve added (or someone else has) that is putting a 150px margin on either side of the calendar (the #tribe-events-content div to be specific). This needs to be removed so the calendar is full width. There may be some other things but that’s one of the most obvious. This is nothing the update would have done, it must be something else that changed that prevented these issues from showing before.
As for getting the calendar on the home page, the only way to do this is with a PHP include that you place somewhere in your theme’s templates (probably page.php) like so:
include('wp-content/plugins/the-events-calendar/views/gridview.php');
I hope that helps but let me know if you need anything else!
– Jonah