salam...my question is that What kind of relationship are young Muslim boys and girls allowed? and for a Muslim boy how can he talk to a Muslim girl?
no relationship between non-mahrams.
Remember islam does not allow free mixing of Non-Maharam boys and girls once you hit puberty.
Quran [33:59] O Prophet, tell your wives and daughters and the believing women that they should cast their outer garments over their bodies (when abroad) so that they should be known and not molested"
Quran [24:30] Say to the believing men that they should lower their gaze and guard their modesty: that will make for greater purity for them: and Allah is well acquainted with all that they do.
Quran [24:31] And say to the believing women that they should lower their gaze and guard their modesty; that they should not display their beauty and ornaments except what (must ordinarily) appear thereof; that they should draw their veils over their bosoms and not display their beauty except to their husbands, their fathers, their husbands' fathers, their sons, their husbands' sons, their brothers or their brothers' sons, or their sisters' sons, or their women, or the slaves whom their right hands possess, or male servants free of physical needs, or small children who have no sense of the shame of sex; and that they should not strike their feet in order to draw attention to their hidden ornaments. And O you Believers! turn you all together towards Allah, that you may attain Bliss.
Bukhari Volumn 004, Book 052, Hadith Number 250.
Narated By Ibn Abbas : That he heard the Prophet saying, "It is not permissible for a man to be alone with a woman, and no lady should travel except with a Muhram (i.e. her husband or a person whom she cannot marry in any case for ever; e.g. her father, brother, etc.)." Then a man got up and said, "O Allah's Apostle! I have enlisted in the army for such-and-such Ghazwa and my wife is proceeding for Hajj." Allah's Apostle said, "Go, and perform the Hajj with your wife."
AbuDawud Book 002, Hadith Number 0641.
Narated By 'Aisha, Ummul Mu'minin : The Prophet (pbuh) said: Allah does not accept the prayer of a woman who has reached puberty unless she wears a veil.