Earlier quoted context omitted.
Unlikely. Opera Mini works by doing all the rendering on the server-side, and then sending the pre-rendered website to the client. It's not actually a browser, so much as an app that gets screenshots from a server-side browser. Firefox, on the other hand, would be a real browser, running Javascript rendering and Gecko on the phone itself, which would not be allowed. That said, I don't understand why anyone would want…
what about encrypted/secured pages?
Is there any end-to-end security between my handset and — for example — paypal.com or my bank?
No. If you need full end-to-end encryption, you should use a full Web browser such as Opera Mobile.
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 Web page. Therefore no end-to-end encryption between the client and the remote Web server is possible.