When great Alla driven away Adam(s) and Haoa Bibi but what the actually fact of their guilty? Had they done sex?

No Milan. They ate fruit from the tree of knowledge which Allah had forbidden.

This should help answer your question a little more thoroughly:
Creation of Adaam [a.s] and bibi Hawa.... (http://www.123muslim.com/islamic-articles/6819-creation-adaam-s-bibi-hawa.html)

"The tree and the fruit
Adam and eve were admitted to Paradise and there they lived the dream of all human beings. Allah permitted them to approach and enjoy everything except one tree, that might have been the Tree of Pain or the Tree of Knowledge. Allah forbade them they were give abode in Paradise. "But come not near this tree or you both will be of the wrong doers." (2:35)
Adam and Eve understood that they were forbidden to eat the fruit of that tree. Adam was however a human being and man tends to forget. His heart changes and his will weakens. Iblis summoned all the envy within him and took advantage of Adam's humanity to exploit him. He started to whisper to him day after day, coaxing him: "Shall I guide you to thTree of Immortality and the Eternal Kingdom?" He said to them: "Your Lord did not forbid you this tree save you should become angels or become of the immortals." He (Satan) swore by Allah to them both saying: "Verily I am one of the sincere well wishers for you both." (7:20-21)
Adam asked himself: "What will happen if I eat from this tree? It might truly be the Tree of Immortality." His dream was to live forever in the pure innocence of Paradise."
Years went by, and Adam and Eve were preoccupied with thoughts of that tree. Then one day they decided to eat of its fruit. They forgot that Allah had warned them not to approach it and that Iblis was their sworn enemy. Adam stretched out his hand, picked one of the fruits and offered it to Eve. They both ate of the forbidden tree.
Allah Almighty told us: "So he (Satan) misled them with deception." (Ch 7:22) Allah said: "Thus did Adam disobey his Lord so he went astray." (20:121).
Adam had hardly finished eating when he felt his heart contract, and he as filled with pain, sadness and shame. The surrounding atmosphere had changed and the internal music had stopped. He discovered that he and his wife were naked, so they both started cutting tree leaves with which to cover themselves.
Allah the Almighty addressed him: "Did I not forbid you that tree and tell you: Verily Satan is an open enemy unto you?" They said: "Our Lord! We have wronged ourselves. If You forgive us not, and bestow not upon us Your Mercy, we shall certainly be of the losers." Allah said; "Get down, one of you an enemy to the other (Adam, Eve, and Satan etc). On earth will be a dwelling place for you and an enjoyment, for a time." He said: "Therein you shall live and therein you shall die, and from it you shall be brought out (resurrected)." (7:22-25). "