Those headset cups are not part of the frame, they are pressed into it.

Read this: http://www.parktool.com/repair/readhowto.asp?id=127

As far as new forks fitting, you will need a 1 inch fork (the other option is 1 1/8). You may or may not need to replace the whole headset depending on its condition and the kind of replacement fork you get.

Why do you need a new one?