1) Dark matter is one of the few great remaining mysteries of physics. It is also (together with dark energy) the most important mystery in cosmology. I mean: it seems to be ubiquitous in much larger quantities than matter itself, yet we don't know what it is! Therefore, it's something people like to work on.
Also, while we have no good idea what dark energy is supposed to be, we have several competing theories for dark matter that make experimental predictions. In order to rule out theories and get a better understanding of what dark matter might be, we need to make experiments. Since dark matter is one of the biggest mysteries, it's also receiving an important share of scientific attention and since we actually have designs for experiments to try to illuminate the matter, we try to do so.
But why do we need so many different experiments? What does Xenon1T add?
Let's start with general arguments for new experimental designs:
As I said, there are many different approaches to dark matter, which often implies that there are many different predictions that must be tested with different experiments.
Experiments can often only probe a certain "scale". For example, there is no detector to detect radiation at any frequency - you'll need different detectors for gamma rays than for radio waves. Sometimes, a theory predicts only that there should be something in a certain range of energies - but no experimental design can actually cover the whole range, so you'll need a number of experiments.
Experiments can "age" and it might be useful to do an experiment again with updated and more precise equipment and a better understanding of what is going on - especially, when you didn't see what you wanted to see. There is no a priori timespan that defines when it is time to do an experiment again - it could be decades or just a couple of months.
This also means that sometimes, experiments are done not with the clear hope to actually test the physical hypothesis, but to prove that the detector design is working and learn how to enlarge it. This means you'll have a number of "prototype experiments".
Scientifically, it is important to get the same results in a number of differently designed experiments to make systematic flaws less likely. For example, this is done in the LHC with the CMS and the ATLAS detectors. The two detectors work quite differently in many respects but mostly try to detect the same things. In short: Redundancy induced error
Now, what about dark matter?
One of the leading theories is WIMPs. WIMPs (weakly interacting massive particles) would be particles that we cannot see because they hardly interact with matter - but since they are supposed to interact at least a little bit, somehow we should be able to detect them. How heavy are they? That's debated and the best guess seems to be some dozens to a few hundred proton masses.
Xenon1T is not a completely new experiment from what I understand. It is a continuation of experiments specifically designed to test the WIMP hypothesis of dark matter, but it is much more sensitive than any of its predecessors.
Several detectors work on similar principles like Xenon1T, e.g. LUX, but none have the sensitivity of Xenon1T. Therefore, Xenon1T is necessary, because it is more precise and it will immediately be the leading detector of its type. The higher the precision, the less WIMPs are allowed to interact while still being visible for the detector.
XMASS seems to once again be similar to Xenon in how it works, but it is - as LUX - a lot smaller. It is also designed to do neutrino physics and is a lot less sensitive than Xenon1T.
You mention CRESST: This is a completely different experimental design, but it also tests different ranges. Its sensitivity is best if the WIMPs are not really heavy, but only about as heavy as a couple of protons. People don't really believe that, but it is not out of the question. Xenon1T is best at maybe 50 or more proton masses.
DAMA/LIBRA is yet different. It seems to be sensitive for smaller and bigger masses and it claims to have observed dark matter and modulations according to the earth's position in the galaxy (and therefore the "dark matter halo" of the galaxy), but its results have been questioned - especially, some people have voiced doubts that the detector design can really tell us that the detected events are dark matter particles. Results from Xenon T1 would presumably be much less disputed.
Many experiments such as ADMX test completely different theories for what dark matter is. You cannot really compare them to Xenon 1T.
I could go on and investigate other designs. The point is that Xenon T1 is better suited at detection and more precise than any (?) other experiment. Therefore, it's necessary and "least likely to fail" if you want.
Short note on Supersymmetry and other Basic Science:
The same holds true for supersymmetry and/or string theories, since they are (at the moment) probably the best candidates on the way to a unification of gravity and the standard model - a feat which is philosophically very appealing and would resolve several inconsistencies in our world view!
[There is, however, also one element to this that is scarcely studied in physics: There are "hypes" in physics. If you ask: Why do we study string theory instead of loop quantum gravity, the topos approach to quantum theory or one of a multitude of other proposals to explain inconsistencies or open parameters and maybe link gravity and the standard model, while in this case it could be argued that supersymmetry and string theory are the best candidates, it is also true that these theories are "in". If a field of study is deemed important, a lot of people jump on the wagon to get funding and sometimes the topic gets much more attention and funding than it is worth. Physics is done by physicists and physicists are people, which means that sociological factors play a role in the decision which of their questions to pursue. However, the bigger the experiments and the field, the more people from outside have a look and, hopefully, the less likely it's just a big hype.]
2) This question is only partly about physics, yet I believe that physicists have to attempt to answer it.
In terms of technological advancements, there are none that I know of. The primary benefit for human kind is knowledge. Whether the knowledge of what dark matter really is will ever benefit us in any way other than satisfying curiosity is entirely unclear. But that doesn't matter. Science is and must not be done for the advancement of technology - that is what engineering and applied science is for. It must interact with applied science, of course, but it is not done "for" application. Science is done for the advancement of knowledge about nature. Before you ask the question "why should we fund this then?", let me quote the last passage from here that sums up one of the best argument for advancing science:
So let’s be honest: the reason to give money to basic science is the same that should be used to give money to the humanities and the arts: because we are a rich country that can afford to spend a fraction of its wealth on things that are not practical, on continuing the human quest for knowledge, understanding and beauty. That these things matter to people, I mean, taxpayers, is demonstrated by the fact that they keep flocking to art museums, philosophy talks and museums of science and natural history. Because their lives are immensely enriched by exposure to ideas that are not just about curing a disease or putting bread on the table, as absolutely crucial as those necessities are. Moreover, in the bargain we do get to convince a lot of smart people (we call them university professors) to teach our kids about all this wonderful stuff. Occasionally, they may even advance our cures for cancer.
There are many different arguments to be made, but it all boils down to the idea that a narrow economic view does not benefit humanity very much either and the whole debate needs to be performed in sociology, philosophy and science just as it needs to be performed in economy.
