Can I create a shortcut to open my mail on my desktop?

Yes, and you can also configure Chrome to open specific tabs upon launch.
To do this:

  1. Click on the three horizontal lines in the top right corner of your browser.
  2. Choose 'settings'
  3. Under 'startup'
  4. Click on 'set pages'
  5. Type in 'mail.google.com'
  6. Click 'ok'