Is there a keyboard / mouse shortcut for paste in MobaXTerm?
The right click is the shortcut for putty to perform a paste.
Is there a similar shortcut in MobaXTerm?
Found a keyboard shortcut in Settings/Keyboard Shortcuts. The default keyboard shortcut is Shift-Insert which can be mapped to something else.
You can have the right click on the terminal by checking "paste with right click" on the settings window under terminal tab. Then you can use the right click as on putty.
If you have a mouse with a wheel/3rd/middle button you can paste with that as well.