As @YaacovDeane wrote, Rabbi Akiva married Turnus Rufus's wife because he saw in a vision that he was going to marry her after she converted. As to why he may have had such a vision in the first place, Ben Zion Fischler wrote an essay on Rabbi Akiva and his wives1 and brings the Ari in Likutei Hashas, Yevamot, who says:
"היינו דאמרי אינשי רחילא בתר רחיאל אזלא. דע כי רע"ק הוא דוגמת יעקב אע"ה ולכן עקיבא אותיות יעקב א' וכשם שיעקב רועה צאן חמיו כן ר"ע גם כן והנה כשם שליעקב היה ב' נשים כן ר' עקיבא נשא בת כלבא שבוע ואשת טורנוסרופוס היתה כנגד לאה ולכן אמר על ברתיה דר' עקיבא רחילא בתר רחילא אזלא כי אמה בסוד רחל וכן בתה ג"כ בסוד רחל והנה ר' עקיבא הוא ניצוץ מרע"ה ומה שאירע לו היותו רועה צאן של כלבא שבוע דוגמת מרע"ה צאן יתרו ויעקב צאן לבן וכן קחתו את בתו דוגמת רחל וצפורה וקחתו אשת טורנוסרופוס כמו קחת מרע"ה מלכת כוש."
Translation: "This that people say: The ewe follows the ewe. Know that Rabbi Akiva is a typification of Yaakov Avinu A"H and for this Akiva is the letters Yaakov A' [short for Yaakov Avinu] and so, like Yaakov [was] the shepherd of his father-in-law, so Rabbi Akiva as well, and as Yaakov had two wives, so Rabbi Akiva married the daughter of Kalba Savua and the wife of Turnus Rufus was against Leah and for this he said on the daughter of R' Akiva The ewe follows the ewe for her mother was a part of the secret (sod) of Rachel and her daughter was also in the secret (sod) of Rachel and R' Akiva is a spark of Moshe Rabbeinu A"H and what happened to him in his being the shepherd of Kalba Savua in a typification of Moshe Rabbeinu A"H the flock of Yitro and Yaakov the flock of Lavan and so also his taking of his daughter a typification of Rachel and Tzipporah and his taking of the wife of Turnus Rufus like Moshe Rabbeinu's taking of the Queen of Kush.
It seems that according to the Ari, the reason Rabbi Akiva married the wife of Turnus Rufus was because of his connection to Yaakov and Moshe; his life reflected their lives and this was a continuation of that "trend", so to speak. Perhaps this is the reason he received a vision that he would marry her, to push him to do that, as a continuation of his life reflecting those of Yaakov and Moshe.
This Ari also seems to answer the other question: Yes, he was married to both at the same time, much like Yaakov was married to Rachel and Leah at the same time.
1 I found it on the site of Haaretz, which is a subscription site, but the essay can be seen for a few moments before being blocked.