Telepathic Communication, do Buddhists Believe in it? I know that Buddhists practice compassionate mediation by wishing to free first their loved ones from suffering, than their friends and than the people they have trouble with. Is this only for the individual practicing or can the practice actually reach the object too? (ie. friend)

ps: There is recent scientific evidence for ESP or telepathic communication but did the Buddhists monks know this whole time? thanks.
It is a well known super power attained by advanced meditators. You can find references to such powers in the stories of the Buddha, and in biographies of well known monks.

Kevatta Sutta:


  "Kevatta, there are these three miracles that I have declared, having
  directly known and realized them for myself. Which three? The miracle
  of psychic power, the miracle of telepathy, and the miracle of
  instruction.


In the Theravada tradition the Visuddhimagga is well known for speaking directly about mastering the occult powers, and in the Madhiyamika tradition (Tibet) the path of the Bodhisattva requires learning to see into the minds of others so they can be helped. 

Accounts from recent times, such as the biography of Ven. Acharya Mun Bhuridatta Thera include incidents where he communicated with other monks living elsewhere.

Ajahn Chah's telepathic powers: https://youtu.be/mPIJhO8ipgs

The Buddha forbade speaking about or giving importance to powers with good reason, so in general accounts are not first person, but third person where a monk (usually) talks about witnessing another's powers.