How do I make the calendar (from calendar app) automatically resize to fit the space on the dashboard?
The Calendar App has a minimum size it can be displayed on a Dashboard (I presume you're using a Published Link in a Web Content Widget, is that correct?). To find this size, expand out the bottom right corner of the widget until the full calendar is displayed, then slowly drag that corner back in, right until it starts to bring in the scroll bars as you have now.
At this time Smartsheet does not have the capability of having published links from the Calendar App resize any smaller than that minimum size. Please submit an Enhancement Request when you have a moment!