If a person invented something new but didn't file a patent:
Is it legal for other people to file a patent for it?
Is it possible for other people to be granted a patent for it if they are not the original inventor?
If other people file a patent and claim they invented it independently at about the same time, what evidence do they need to show?
If the original inventor has clear evidence to prove his/her originality, is there a way to stop other people from patenting this invention?
The US uses a "first to file" system, or maybe more accurately, "first inventor to disclose" system. If two people independently invent the same patent eligible thing, and neither discloses it publicly, then the patent will be awarded to the first person to file.
To prevent somebody else from patenting your invention, either disclose your invention publicly or apply for the patent yourself as soon as possible.
The entire premise of the patent system is that you disclose your invention to the public in exchange for a limited monopoly on the invention. If you invent it early and keep it to yourself while someone else goes ahead and invents and patents it later, then they are the person who has undertaken to take advantage of the premise of public disclosure through the patent system in exchange for patent protection, so the patent system protects them, not you.
The patent system also requires that the inventor file for or have assigned his patent rights. Someone else who steals your invention cannot get a patent on it, or at least if they do the patent will not be valid and enforceable. Issued patents are presumed to be valid, but you can still show they are invalid, and one way to do that would be by showing that they name someone who stole the invention as the inventor.
