What do you need to be pressing to open all of the selected players/etc as new tabs simultaneously {from a list}? I keep hitting this randomly but never can find out what is the shortcut?

If I think you mean what I think you mean, you press 'Select All' from the Team page.  That will bring up the tabs.

That is kind of what I meant - there exists some keyboard/mouse combination that does the identical thing but only for selected players.

Press the Control key and click the players you want, then right-click the selected players and click Edit if it is there.  Or you can just double-click each player and they are added as a tab.

I explain how to do this in the FAQs in the preset explanation