I usually understand "dark matter" to be shorthand for the discrepancy between theory and observation. The explanation might indeed be matter that is dark, or it might be solved by entirely unexpected observations and/or changes to theory.
Not really. You might think this after watching Angela Coulliers video, but when you read something like "25% of the universe's energy content is made of dark matter", they do not mean changes to some theory. They literally mean non-baryonic matter.
Nope. It can mean change to some theory, without a need for matter. It is the difference between relativistic gravity and the corresponding observed mass.