I suspect you've probably figured this out by now, but if you want content that is laready placed in many documents to update, it should be linked to a n external file. Libraries are not good for this. Just place you .ai file or other image. If it needs to be changed across multiple documents, use Edit Original and it will update inthe current document, and other documents will alert you when opening.
Does the file need to be created in Illustrator? I have some content elements that basically contain some text and boxes. So I am wondering is this still the best way? Sounds like I cannot create the library element in InDesign.
Also, I was told that another possibility is to create a page for that element, then place it in the InDesign file. Would that work as well? I basically have about 20 different design elements that I want to use in various documents. Since they would likely change it makes sense for me to have the capibility to edit the document once.
You CAN link ID files.
A library is a place to go to get elements for use... but they are NOT linked to it.
As Peter said, you need to place the graphics (via file > place)... then all you need to do is update that graphic and all linked files will update (when you open them).