You could use the Menu attributes module to add classes to each module (such as top-left, bottom-right, etc) and style based on those. This will be a lot more robust than using ids derived from the menu link's mid.
Next, to get the links to the corners of the screen, you will need to give them position: absolute or position: fixed. Bear in mind that that will allow you to position them relative to their first positioned (not static) ancestor element. This means that you'll have to make sure that none of the containers around the menu links have a css position of anything other than "static".
Finally you may need to add "min-height: 100%" to the html and body tags in order to make sure that the bottom-left/right links do get down to the bottom of the page.