You hear the other person's voice in your head. It's kind of disconcerting at times if it is particularly loud or bothersome or cruel or intending to disturb you.
It can happen. You can pick up the thoughts of another...sometimes even an animal. There are usually what are termed "senders" and "receivers".
A person can possess both talents.

One must learn to shut off this ability. Hearing everyone's thoughts can make you crazy. Not everyone can send their thoughts, which is good, and hardly anyone can receive thoughts. You can sense emotions, however, and sense when someone is lying, but that may just be the ability to read body language extremely well.

A person who has this ability is termed "sensitive". As a sensitive person, one is prone to be empathetic and empathic. Funerals are terribly bothersome if there is a great deal of weeping and hard feelings toward the deceased. Good time, though, are even better if you can pick up everyone else's happiness.

As for sending thoughts to a particular person, I suppose if you were in tune with that person and easily picked up their thoughts and impressions, not even a great distance separating you would matter.
By and large, though, only great trauma can be transmitted over distances.

That "bad feeling" of something coming is clairvoyance. Seeing what is happening as it happens is the result of telepathy.

Reading the minds of others is a double edged sword. Sometimes it can be equivalent to "the force". Other times, it comes too little too late to do anybody any good. When somebody else is thinking of doing something, they're probably already engaged in doing it.

Could come in handy during a math test, however.