Would you?

NO

You will need to prove it.

It really depends on the person involved.  Young children have been seeing "invisible friends" for eons.  There is currently a tv show on that I think is excellent that helps youngsters with mediumship and healing abilities to not only come to terms with their abilities under a certified medium and healer, but also helps their parents come to terms with this ability and to make them realize that the kid is not "nuts," but has real abilities just like somebody who has musical abilities or other types of abilities.  Having said this, for years there have been charletans who say they are mediums or can foretell the future which are frauds.  Then, not everybody can actually "read" for another person.  I can tell you having worked in the field since I was 14, there are many, many people out there, especially parents that always know when their kid is in trouble before they even get the dreaded phone call.  When I was growing up it was called "being in tune" with the kids.  Now, it sounds like I'm waffling here, but the truth of the matter is that many people have so-called "supernatural" or "paranormal" abilities whether they choose to call it that or not.  Just like anything else they can be more or less developed in different individuals.  If a person told me that they had this type of ability, I would probably want to question them further to see if it is legit, how long they have been experiencing them and whether they seemed grounded or not.  On top of this, certain types of mental illness can bring out a delusion of having an ability that one may or may not have (hence, the questions, lol).  Bottom line is, I would have to see them in action and have them demonstrate their abilities for me in an appropriate format for that ability. 

Sometimes yes, sometimes no. For me, I believe then if they are talking with pure sincerity. (Note: You can really guess if a person's sincere or not according to their eyes or how they talk)