MacOS – Pages question on Apple yosemite

Someone has to give you the bad news:

You can't. You have to copy/paste and re-edit again in the other mode. When you create a new pages document, you have to wisely chose the one that suits you best. You can’t go back and forth between them nor mix the types in the same document.

Sad but true. ;)

Simple. Make sure you've selected the object you want to remove the line from. Click your inspector, and navigate over to the graphic tab (see screenshot). select none. Last screenshot shows the result.