"It is important to take notes."
When used like this, の is what's called a nominalizer. It turns the first part of the sentence, ノートをとる, into a noun so it can be used with the は...です sentence format. It's a bit like saying "the action of [whatever precedes it]."
Should it be ノート and not メモ？ Every time I used ノート like this in Japan they got confused and said I should use メモ and that ノート was more like a notebook.
たいせつ should be one word. Separating just つ on a different tile is stupid and makes no sense. The Japanese course has a big problem with splitting words up that shouldn't be split up. This does nothing to help learners and makes things needlessly difficult for them. The French course at least doesn't have this problem.