Are Muslims allowed to have extra marital affairs?

I think not, am not sure aim, Because if They Are not allowed to relations outside of marriage Have, then the suicide bombers Why Do THEY think That Will Have 70 virgins in heaven, That Would Be as a sin. . If Someone Could explain this thinking?

Can muslims, who have committed adultery in the past and then repented marry virgin muslim women?

I want to know that these Muslims who committed adultery in the past and repented are they still entitled to marry a virgin Muslim women? Does Islam allow this?