Talon, let this by my only religious lesson on this forum. I shall never indulge again in such an activity.
First of all there is no reason to explain Surah An-Nur Ayat 31 to you, you're intelligent enough, read it over and over again, and conclude what your mind tells you, Allah will judge all by their own abilities of comprehension, however, if you still want I can highlight the parts that you need to focus on.
Now, regarding Surah Al-Ahzab ayat 59:
At the time when this particular Quranic ayat was issued, Muslims of time used to live in closed communities within walled cities.
There was no proper sanitation system @ homes of individuals, hence the need of "public" toilets. Now second thing, at the same time there were two different kind of women @ households. 1. Wives, sister, daughters 2. Keeps (whatever you want to call them) Now read the Ayat again, what does it say? About which women? When these women in the darkness of the night used to go out to the toilets, there were street-men and boys who used to annoy these women, without distinction between the two groups. Now once again read the Ayat. Did you get it? Or do I need to go into further detail with you. There is one corresponding Hadith to this Ayat, if I tell you, you'll be shocked!
Similarly, I can debunk different Hadith with you (though I only trust Quran). Don't judge me by my oh-so-open-liberal attitude, if necessary, I am fit to give a sermon!
Timing and purpose is everything in Islam, what time was an Ayat revealed and why, try to get this concept instilled in your logic processor!