How can I use "three buttons button" using just keyboard? I think Enter should at least run the default option (like left mouse button).
I don't think you can. Three-Buttons are made for mouse use. If using the keyboard, normal toolbars/menus/accelerators/hotkeys are a better way to do things.
Maybe you could implement
Enter = LMB
Ctrl+Enter = RMB
Shift+Enter = MMB
or something similar?
I like to hide less frequently used functions under three buttons and don't like menu buttons as the arrow to expand menu is too small and inconvenient for me when using mouse.