Yes, the Google Task gadget is available in Gmail and Calendar.
Yes, Gmail includes a full set of keyboard shortcuts. First, you must enable keyboard shortcuts: In the upper-right corner of the Mail window, click Settings. Under Keyboard shortcuts, select Keyboard shortcuts on. Click Save Settings. Then, to see the shortcuts, press SHIFT + ? while viewing your list of messages in the main Mail window.
Yes, in Gmail, you can set up your "vacation responder," which is similar to the Out of Office feature in Outlook or Lotus Notes. For details, see the Gmail Help Center.