QuickPar: Have you turned on the option in Opus to "hide Windows items on context menus?" If so the QuickPar item will only appear if you hold shift when you right click (or turn the option back off, or if you force its item to appear, as described in the tutorials section of the forum).
FastStone: Try using the Open With menu to associate FastOne with the filetype. That should make Opus recognise the association if it hasn't already.
Modified column: Go to Settings -> Preferences -> Display -> Fields, select the Date and Date/Time fields and set the Reverse standard sort direction checkbox for each of them.
ListerMenu: If the hotkeys are defined in a menu/toolbar and you close that toolbar then the hotkeys go as well. If you don't want the menu/toolbar but still want the hotkeys then you have to copy them to standalone hotkeys. You can do that in Settings -> Customize -> Keys.
Vertical drive buttons: Just drag the toolbar between the tree and the file display.
None of these things are new behaviours but they're all solvable anyway.
General: Please ask one question per post, if the questions are unrelated.