Try making a test standalone installation of Opera Developer. Download the offline package from the developer section at https://www.opera.com/download.
If that test Opera developer installs and runs fine, close it. Then, in its install folder, there will be a profile/data folder. In it is the "Local State" file. And, in the "Default" folder there, is the "Login Data" file. Replace those 2 files with copies of the ones in "C:\Users\yourusername\AppData\Roaming\Opera Software\Opera Developer".
Then, start that test Opera Developer and goto the URL opera://password-manager/passwords to see if your passwords are there. If so, goto the URL opera://password-manager/settings and export your passwords to a CSV file.
Once you have the CSV file, whenever you get your regular Opera Developer up and running again (by starting with a new profile and cache folder maybe), you can goto opera://password-manager/settings and import that CSV file.
As for speed dials (which are bookmarks), you can copy the "Bookmarks" and "BookmarksExtras" to the test Opera developer (choosing to overwrite the existing ones there) while that test Opera developer is closed. Then, when you start it, you should see your speed dials hopefully. You can then goto the URL opera://bookmarks and use the drop-down at the bottom left to to export your bookmarks to an HTML file. Then, in your regular Opera developer (when you get it working), you can goto the URL opera://settings/importData, choose "Bookmarks HTML file" in the drop-down and point it to the HTML file. Then, you can goto the URL opera://bookmarks and get the speed dials from the "imported" folder in the "bookmarks bar" folder, select them and move the selection to the "Speed dial" folder.
Or, another way to try things it to make a backup of "C:\Users\yourusername\AppData\Roaming\Opera Software\Opera Developer". Then, in "C:\Users\yourusername\AppData\Roaming\Opera Software\Opera Developer", delete everything by the "Local State" file and the "Default" folder. Then, in the "C:\Users\yourusername\AppData\Roaming\Opera Software\Opera Developer\Default" folder, delete everything except for "Login Data", "Bookmarks" and "BookmarksExtras".
Then, Opera Developer should start mostly fresh except retain your passwords and bookmarks (speed dials too) as long as they're still in the files.
You can also try uninstalling again, deleting the Opera Developer install folder afterwards and then using the offline Opera Developer installer to reinstall.
All kinds of things you can try as I'm not sure where the issue is.