Notes section should be included in the mobile version of Duolingo.
Having additional information about how to uses certain words or how to form certain sentences is very important, and I think including that in the app will be very convenient because you can learn on the go.
Yeah, I agree. I've been using this Duolingo Notes Wiki: http://duonotes.wikia.com/wiki/Duolingo_Tips_and_Notes_Wiki
in the meantime, but it would be nice to have everything on either the mobile site or the app.
Yes they should... but the fact that Duolingo splits its features between the app and the site suggests me that they want you to use both platforms. As a complement if you will.