I think you ought to be able to stick the pin back in- they are usually removable.
OR if you know what you are doing (contrary to present evidence) then cutting off the damaged plug and installing a three-prong, UL-approved replacement plug would work as well.
Yes you can, but it might not be safe. The top plug is the Earthed/Ground port- so if any voltage is leaking out to the surface of your computer, you might get a shock..
Where does the third prong go in the power adapter extension cable? When the power brick is used without the extension cable, there is a little two prong attachment and there are two posts that connect to the power brick. With only two posts to connect to where does the third prong go/what is it actually doing?
Hard to describe without visuals.. the ground pin makes contact with that big metal "button" that you clip the exchangeable attachment to. if you look inside the "slot" of the extension attachment you'll see the contacts. The third prong is ground.