You ask a number of questions. I'll try an answer them.
Yes, galaxy clusters (except the one we are part of) are many millions of light years away and so the neutrinos from them (which travel at a speed only a tiny fraction below that of light) have taken millions of years to get here. However, the light from those clusters has also taken millions of years to get here, so if we look in a certain direction and see a galaxy, and we detect a high energy neutrino coming from the same direction, then the galaxy was there when the neutrino was emitted (or passed through it). It may have moved since, but that would affect neither the light nor the neutrino.
Neutrinos are affected by gravity, and so the neutrino images of distant objects can be distorted in the same way as the optical images when there is a massive object (like another galaxy cluster) between it and us. However, if that were happening, we would see the distortion of the optical image.
It is also possible (though extraordinarily unlikely) that a single neutrino might have been deflected by passing close to a very massive object such as a black hole which is too small to make much of a difference to the optical image of the cluster. The chance of a neutrino from somewhere else being deflected by something we haven't detected, just enough to appear to come from a galaxy we can see, though, is absolutely amazingly minute. A bit like a bullet ricocheting off a falling meteorite in such a way that it seems to have come from that man over there holding a gun, even though it actually came from somewhere else.
Finally, on the question of detection. It is true that neutrinos interact weakly with matter, but these very high energy neutrinos interact less weakly than others. This paper and in particular its figure 1 suggest that neutrinos of the energy reported ($2\times 10^{15}$ eV according to the article you refer to) would interact about 10 million times more strongly than the ones from the Sun or from nuclear reactors. Even so, most neutrinos will go straight through ice cube without interacting with it at all, despite the fact that it consists of a whole cubic kilometer of ice. Of the few that do interact, the interaction will usually "kick loose" a charged particle (often a muon) from the ice, which will be moving at close to the speed of light (in vacuum) itself, and in the same direction that the neutrino was moving. In particular, it will be moving faster than the speed of light in ice. When a charged particle moves faster than the speed of light in whatever material it's passing through it produces a "shock wave" of light, called Cerenkov radiation. Detectors in ice cube pick up that radiation and track the movement of its source, thereby getting a good idea of the direction from which the original neutrino came.
