It looks like you have two copies of the library: one in the sketch folder and another installed normally. That will cause a multiple definitions error.
You should be able to fix it by simply deleting the library files from the sketch folder.
If you will post a link to where you downloaded this sketch from, we might be able to provide you with more effective assistance.
That's normal and expected. Library Manager is only used for managing the Library Manager libraries. You will not see the libraries that you installed via the "Add ZIP Library" menu in Library Manager.