Does talaaq take place through separation

Q: A guy and a girl got married. They had an arguments and then girl left the house of guy and stayed at her parents home from June 10th 2016 to Jan 23rd 2017 during this period the guy never pronounce a divorce "Not even single time" The Girl stayed at parents house for more than 6 months and there's a person who said that according to Islam if you stayed away from your husband for more than 6 months without any Sharai reason then you are no longer in Nikkah with that guy. (who said not sure, on what grounds not sure) Need clarification on this as well. The Guy sent Divorce deed on 23rd January 2017 that has clearly mentioned divorce Thrice upon that girl, the guy who sent divorce deed was planning to end the marriage because of girl's parents demand. Now, the concern is. If 6 months were already passed while girl stayed away from here husband. Then she was no longer in Nikkah of that guy and so does divorce occurred? IF YES then how? IF NO then why?

What will women get in Jannat?

Q: I'm a practicing Muslim woman in USA and I notice that in the Quran even if the men are rewarded with Hoor Al Ayn there is no stated reward for women in the Quran. Like sometimes I need motivation for Jannah and saying "whatever you desire" is too vague for me. Maybe if Allah stated that women would be rewarded with a palace with singing angels or a Pegasus or a personal spa it would have motivated us even more. So I could pray five times a day and at the end of the day I could say Allah would reward you with blah blah blah and I could say Allah is very generous with me or I could be very happy knowing I won't be disappointed in the afterlife. I know Jannah isn't like Dunya, but how Allah reassured the men that even if they died unmarried or withheld themselves in this world Allah will substitute with something better, sometimes I need the same reassurance. Also I think a lot of Muslim women need reassurance also. What do women get?

Giving azaan and iqaamah when performing salaah at home if one can not hear the azaan

Q: In my area, the nearest masjid is about 10kms. There is also a musalla nearby but azaan from the masjid or the musalla is not heard. However, for several reasons, I have to perform salaat on my own at home and, in the circumstances, is it imperative to give azaan and recite iqaamat before salaat? Does this also apply if one is also performing missed salaats?