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Of course it is. It already passed many tests (for example gravitational lensing) while some dark matter candidates (WIMPS, primordial black holes) have effectively been ruled out through tests.

Dark matter is not a theory, per se. There are many, many theories that attempt to explain dark matter. Some of them have yet to produce testable hypotheses, others have already been tested.

Thank you. Dark matter is the issue in cosmology that "it appears as though undetectable matter is present in the universe causing X, Y, Z phenomenon."

The issue that I have with people calling dark matter a theory is that they think it requires matter to solve. It doesn't. MOND is a dark matter theory. It explains(in part) why it appears as though undetectable matter is present in galaxies causing disc velocity to not match expectations.

It's not, but it's accepted as it is the theory that best fits the observations. It has holes, but not as much as others. It will continue to be the accepted model until another one is an even better fit to the data or we can prove/disprove the existence of dark matter.