In case of Opera Mini client part of browser does not have technical ability to parse and render html.

Does it have the ability to access HTTPS content?

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.