Re: how to use the knife tool ?
The Knife tool is best used with a rectangle (think like a knife blade) - it's the surfaces that do the slicing.
Perhaps you want the boolean knife. You'll need to ensure the "knife" object is closed and the normals face outwards. On the model you show, Object->Fill-hole should do it. Press 'n' to show normals and check they are all outwards.
Then you can select the sphere, followed by the knife shape and use Object->Boolean->knife, of any of the other boolean functions.
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