A hoax is something that encapsulates the idea of deception, typically on a large group of people. Often there is no element of humour in a hoax, instead the principle aim is to confuse or scare. A hoax normally has long term consequences and mysteries that are never resolved. This has created many modern day 'legends' e.g. Loch Ness Monster, Bigfoot, Roswell, etc.
- something intended to deceive or defraud:
Example: The Piltdown man was a scientific hoax.
A prank on the other hand describes a (often lighthearted) trick played on someone you know, or on a small group of people. Typically involving some kind of physical humour intended to temporarily confuse or scare someone. However, a prank can also take on a darker sense of humour too. A good example of the spectrum of 'darkness' would be convincing a friend that their dog has died vs pretending to be a statue and then jumping out at people.
- a trick of an amusing, playful, or sometimes malicious nature.
As for your last questions, you can definitely play a hoax on someone. Hoax itself is also a verb so in some circumstances it may just be simpler to use it that way.
It also makes sense to say that UFO stories are a hoax. Although a small pedantic point: the concept of UFO stories is not a hoax in my opinion as they cannot be pinned down to a single event and are by definition 'unindentified flying objects'. You could certainly say something more specific like "crop circles were the biggest hoax ever played on extraterrestrial believers".