A bit of lore:

Why most Otherkin can reproduce with humans:
Long ago, spirits came to Earth to possess animals, as they could naturally produce energy that the spirits could absorb. Many of these animals were mutated by the spirits and, by biokinetically altering their DNA then selectively breeding them, they created new breeds, many of which became mythical creatures. Eventually, a new race evolved, humans. Unlock the other biological lifeforms, they had abilities which the spirits could copy if they possessed them and used them enough. They had several shortcomings, though. Physically they were weaker than many animals, they were more difficult to possess, and their powers were impossible to predict. In order to know what they could do you either had to find one of the few that had powers or you had to possess them and unlock their powers. In order to fix those weaknesses, they did the same thing to humans that they did to animals, only you couldn't leave a human once it had powers or it could be a threat. For this reason, and to prevent inbreeding from having a too limited gene pool, they formed groups with similar interests in a host. These groups, dozens or hundreds in size, created the their own breed of what they considered the perfect host, like breeds of dogs.
Eventually they abandoned their host for the most part, finding other worlds and dimensions with better hosts. Their former host species formed their own cultures and societies.

How to get powers:
1) Genetics. Most Otherkin and some human bloodlines have this trait.
2) Enter subspace (not-space). Very rare, and the only species that uses it for teleporting are Seraphs. Used by Watchers (the Roswell aliens) on children that don't develop telepathy within a month of birth. Only works on Telepathy, Telekinesis, and Spirit powers.
3) Get possessed. Most spirits unlock your powers when they possess you, and when they are being exorcised locking your powers down is a low priority, especialy if your powers are useful in stopping the exorcism or fighting it.
4) Be exposed to a closely related power.
5) Surgery. Current techniques developed by the USSR during the Cold War.
6) Some powerful telepaths can unlock powers. Some branches of the BPI have such telepaths on the payroll in case they recruit someone without powers, or someone's powers get taken away or locked.