I am running 37.0.2192 on Android 5.0.1
In Android application settings, Opera DOES have permission to "modify and delete the contents of your SD card"
But when I attempt save content from a page, Opera does not allow me to select the SD card. When browsing "/storage/sdcard0" (which is really onboard phone memory) the "select folder" button is clickable, and I can save there. But when attempting to save to the path "/storage/extSdCard" the "select folder" button is dimmed out and not clickable.
I realize this was probably caused by Lollipop Android 5.0 release when SD card perms were completely reworked, but that was released in late 2014. I am surprised that 20 months after that change this is still a problem in Opera.
Also, when I attempt to use the search box on the site here, it does not search anything. It simply takes me from whatever forum page I am on and sends me back to the forum index https://forums.opera.com/. That seems to need some attention.