I've got a google calendar and i have tried personally Gcalndar extension to see occasions on my small website. Is it feasible in some way will be able to send the all joomla customers an e-mail about new occasions from google calendar

You would not have the ability to get it done through Google Calendar unless of course you export a listing of emails then paste that list to the visitors box in case particulars. That might be quite a large discomfort to complete each time. It might most likely be considered a lot simpler to make use of one of the numerous e-newsletter management extensions to transmit out event bulletins with the Joomla site. A lot of options within the JED here - http://extensions.joomla.org/extensions/content-sharing/newsletter