Yes, but Opera basically say that there are using a MITM approach:

> 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/#security

Yes. If you read the terms of service for the Opera Mini browser, they disclose that HTTPS sessions are not end-to-end.

It also requires you to OK through a warning the first time you access an HTTPS site, so it's not a fact that's buried in some legalese.