What combination of keys produce a right-click and a left-click?
There isn't one for left-click, though spacebar and Enter are often usable.
Right-clicking is usually a request for a context-sensitive menu which is performed on the keyboard either by typing
≣ Menu key (https://en.wikipedia.org/wiki/Menu_key),
or sometimes Ctrl+Shift+F10.
About 65% of applications out there won't respond to the keyboard request for a context menu, because Windows programmers typically code WM_RBUTTONUP rather than the correct WM_CONTEXTMENU. Coding the latter allows for the correct action in response to the keyboard.
I have a new Logitech K740 keyboard. It just replaced my old Dell letters-scratched-off key board that had built-in context menu selection and calculator shortcut keys.
The solution to the context menu issue on the Logitech K740 is FN + PrintScrn (shows a little page or list). This key combo pops open the context menu.