Although they make good topics for science fiction, there is no reliable scientific evidence to support any of the various branches of the paranormal. Although there has been some very convincing individuals that demonstrated apparent telekinesis or telepathy, people like the Great Randi have successfully debunked every case to which they have had unfettered access.
The fact that there has been no unchallenged scientific support of the paranormal does not mean it is not an active area of research. There are institutes that support such research. Whether their results are reliable or not will eventually be up to peer review.
Kind of. That is to say, there is scientifically collected evidence related to supposedly paranormal activities. However, chances are the evidence is not really describing or proving what the scientists collecting it think it is proving. There is nothing convincing.
There have been studies conducted for many decades now, such as the Ganzfeld experiment at Cornell University linking the certain psychic paranormal activities to dream and hypnotic states and the PEAR experiment at Princeton University linking human consciousness to interactions with "sensitive physical devices, systems, and processes." But these studies are for the most part--rightly or wrongly--discounted by the majority society. It's an odd human trait that if it isn't tangible and tangible on the surface of or in the bedrock of the planet, it is unbelievable.
Certainly people have been convinced of what we would call paranormal activity actually occurred. Science, which is concerned with searching out the truth, can only say that "someone experienced something." Hypotheses may be stated; with enough evidence and experimentation, some facts may ultimately be able to be derived.
We may get a better understanding of such things as science continues to understand Quantum Mechanics. What is unexplainable and unsubstantiated today may, someday, be able to be quantified, measured, and understood through the Scientific Process. Right now, we're not quite there.
The military did a decade study on "remote viewing". While it doesn't prove anything, it is suspect that it would continue for so long.
You should know that science is not impervious to politics. You have respected scientists with theories to protect, which can prove difficult to overcome if you have a theory that opposes theirs and, subsequently, those who base their theories on that scientist's. Also, the term "peer review" is represented as synonimous with objectivity, leaving many to believe that it is truth. However, one can see how this can be corrupted although few question. Medical journals are loaded with pharmaceutical ads which are their main source of revenue in most cases. It is easy to see a conflict of interest a medical journal would have in publishing a study that found a particular drug or treatment was detrimental to health. For example, cannabinoids (chemical compounds found in marijuana) are shown in many studies to reduce many forms of cancer tumor growth. Why is this not known by the mainstream? I believe it is because a plant cannot be patented and it would compete with other expensive treatments sold by big pharma.
Do the investigation yourself looking at both sides of the issue with as much bias set aside. While it may take you a while to weed through the data, the investigation on any theory should bare fruit in one form or another. Who knows, you may come up with your own theory. Cheers.