Right click the link and click "Save linked content as..." to download MP3 files. Or any files really.
The search engine complaint is well known and the devs do know about it. I don't know if changes are coming or not but they have said that it is the way it is (hard coded in a file) because it helps protect against malware hijacking your search providers. I work as a computer service tech and I can attest that browser hijackers are a really common problem. How effective Operas defense is I cannot say as I have yet to run into a user that has that kind of malware and uses Opera.
As for 'integrating' Webkit into Opera that is not what has happened. Presto wasn't removed from 'Opera', 'Opera' was discontinued. A brand new codebase from the ground up was created using webkit. That is why everything has changed; because there is literally no code carried over. They are basically two different browsers, both named Opera, bother made by the same company, but completely different programs.