Kimmer, have you gone through Opera's preferences - particularly the Windows one and the Start/Exit preferences to see if there is anything there that might be doing this? Mine is behaving itself - window is opening in the top right of my screen every time. I do NOT have "show saved window setup" checked in the preferences though - I have "show home page". Maybe you should try that and see what happens?
Opera still doesn't work on some pages for me - if anything is not going to work, it will probably be in Opera...sigh. The only browser that doesn't work with the Javascript that both Jennie and I have been using for slideshows is...Opera.
Have you tried Camino or Omniweb? Or iCab? Or Mozilla? Go to VersionTracker.com, click on the OS X tab and then do a search for "web browsers" - you'll get all of them and then can download 'em and try 'em. I have them all. I check all my web page designs in all of them...helps find problems (though sometimes it's the browser, NOT the person doing the coding!) All of them will run on earlier versions of OS X. Of course, Safari reigns as far as I'm concerned, but you need Jag to run it.