The 3rd Party App automatically saves the last Position of Every Window, Folder, etc. when its Last Instance is closed. There is no switch for Opera, nor any other Program. It is always running in the background.
Opera is started from a Desktop Icon. It is simply C:\Users\UserName\AppData\Local\Programs\Opera\launcher.exe.
Yes, sorry. Task Bar.
Only IE is pinned, as it is used infrequently with older Programs which fail without IE.