There are multiple lines of evidence for the existence of effects caused by something we label "dark matter". These include the orbital speeds within galaxies, the speeds of orbits with galaxy clusters, gravitational lensing, the spectrum of the CMB, the formation of large scale structures in the universe, and probably more.
Nearly all of this evidence points to dark matter being a form of matter which does not interact electromagnetically. So, similar to neutrinos but it must be more massive because the distribution shows it to be moving more slowly.
Not "see" it because it doesn't;t interact with light. I guess the question means will we ever have a more "direct" detection of the particles that make it up? Probably.
It took over a decade to detect neutrinos "directly" before they were first detected. Obviously, it is harder to detect dark matter particles (otherwise we would have known what they were, perhaps even before observing the effects). It is rather inevitable that each new type of particle is going to be harder to detect.
I don't know what that means. Neptune was a "wildcard thrown in to a mathematical equation to make the equation work". The same could be said of electrons, photons, gravity, energy ...
Physics is described in terms of equations. When we discover new things, they are are included in those equations.
That would be true whether dark matter is a modification to gravity or some form of matter. So the question doesn't really make sense.