以下のとおりお答えします。(最初の文は意味が不明でしたので、勝手に補充・書き換えさせていただきました。これでよかったのでしょうか?)
"They're harmed by domestic violence in recent years. The lady who associated with an American man was executed with him in public."(近年では、彼女らは家庭内暴力でいためつけられています。アメリカ人男性と交際した女性が、その男性共々公開処刑されました。)
"Now, we'll decide the future by our own power. Dreams can be held freely. An ordinary thing for us is prohibited in Saudi Arabia."
"Those ladies who were under such condition have come to be allowed to drive a car and to vote in election from this year. Though the restriction is still severe but is changing little by little."
以上、ご回答まで。