I am using Opera One and have this problem too. I found that I can copy the URL in the usual way then in a new opera window click File/Paste from the top menu. Somehow right click on a mouse doesn't work. Hope you found a workaround.
@aridajd@Starsiege-Mercenaries What version do you have? Please check that it is at least 102.0.4880.40. The button has been fixed in this version. And, as I wrote above, the close button is also not stretched to the very corner, so you have to hit it, which is inconvenient.
There's no option to have PDFs automatically open in the default PDF client after they're downloaded. The only option you have in Opera is at the URL opera://settings/content/pdfDocuments where you can choose to download PDFs instead of having them displayed in Opera.