I moved my Opera installation across to another hard drive (just by copying it). This lost all the settings, mail, bookmarks, etc. I logged into Opera Link and found a list of all my bookmarks. Is there a way to actually import those bookmarks into the browser or download the list? My browser version is 12.15 (I only want to upgrade if it is the only way to get my bookmarks).

I reckon if you installed Opera anew in that other place then copied your Profile folder there - it could actually work.
Otherwise, if you only need your bookmarks but not any settings, you could transport them via the built-in export-import feature - either with a .adr or .html file.
I don't know much about mail, but your settings must be stored somewhere in (an) .ini file(s) - most probably within that Profile folder it is.