I read the tutorial, https://developers.google.com/apps-script/articles/building-sites-app-part2 that uses spreadsheet service in Google sites. The code uses the spreadsheet key. However to access my mail should I use Oauth or something like,
var email = String(Session.getUser().getUserLoginId());
Can we also use minute trigger when we embed GAS in google sites?
Your question is not clear. What do you want to do ? Do you want to get the email ID of the user or do you want to access your email.
Session.getUser().getUserLoginId() only returns the login id of the logged in user. And it works only in Google Apps accounts (not consumer accounts).
If you want to access your email, then make use of the Gmail service