"Is there any end-to-end security between my handset and — for example — paypal.com or my bank?"
"Opera Mini uses a transcoder server to translate HTML/CSS/JavaScript into a more compact format. It will also shrink any images to fit the screen of your handset. This translation step makes Opera Mini fast, small, and also very cheap to use. To be able to do this translation, the Opera Mini server needs to have access to the unencrypted version of the webpage. Therefore no end-to-end encryption between the client and the remote web server is possible.
If you need full end-to-end encryption, you should use a full web browser such as Opera Mobile."
http://www.opera.com/mobile/help/faq/#connection
"Is there any end-to-end security between my handset and — for example — paypal.com or my bank?"
"Opera Mini uses a transcoder server to translate HTML/CSS/JavaScript into a more compact format. It will also shrink any images to fit the screen of your handset. This translation step makes Opera Mini fast, small, and also very cheap to use. To be able to do this translation, the Opera Mini server needs to have access to the unencrypted version of the webpage. Therefore no end-to-end encryption between the client and the remote web server is possible.
If you need full end-to-end encryption, you should use a full web browser such as Opera Mobile."