Choosing a spouse

Q: I am looking to get married. I am a 25 year old male. I recently went to see a girl and everything about her was good and I feel inclined to accepting her. From her end it is positive too. The only area which is causing me confusion is that although she wears a hijab that covers her hair, neck etc, she does not wear the full abaya. Is this permissible? Would it be permissable for me to marry her if this is the case. I am planning on having another meeting with her in her house in the meanwhile to clarify some more issues and will also ask if she intends to wear one, she did mention that she wants someone to marry who will encourage her in terms of deen. I have also been performing istikhara for over a week and it is all good except doubts on the above question. In my family there is no one that wears the abaya or niqaab, but my mum does wear hijab. I am also trying to encourage my sisters to wear one. 

Memorizing the 99 names of Allah

Q: What is meant by "memorizes" or "preserves" the 99 names of Allah in the Hadith below:

عَنْ أَبِي هُرَيْرَةَ عَنِ النَّبِيِّ صلى الله عليه وسلم قَالَ لِلَّهِ تِسْعَةٌ وَتِسْعُونَ اسْمًا مَنْ حَفِظَهَا دَخَلَ الْجَنَّةَ

Cycling

Q: I am an active cyclist. Crashes are often and we tend to get a lot of cuts and bruises on our body which causes our hair to get stuck to it and infect it. Is it permissible for a man to remove his legs and arm hair in this situation?

Washing a musalla that was touched by a shoe

Q: My mother uses a sandle which she takes to the toilet also. A few times she accidentally stepped on my musallah. I touched the part and it was not wet. With my hand only, I clean the dust without using any water as I am not sure where she exactly stepped on. She also stepped on the musallah with her shoe which she wears when she goes outside. Do I have to wash the musallah? I am currently reading salaah on the same musallah. I have doubts about another musallahs because my nephew urinated on them and the house worker washed them. I dont know if she washed it thrice or not. Can I read salaah on them as she used a detergent?