Well, lemme answer one at a time
I note that Aisha narrated over 2k hadiths, but I don't know what a hadith is.
A Hadit is, well. The Prophet Mohammed did not want his every word written down and memorized, just the Quran. Following his death though, people still felt that God's messanger was the best guide as far as how to live your life goes, so people that knew him, the Sahaba, would recount events and sayings. They ranged from people saying "I heard him say" to people saying, "Well, he said she said that they said that Mohammed said..."
So Hadiths are effectively the second most holy book. Though again, each branch has it's own version, with a minority of scholars rejecting it entirely, because Mohammed didn't want his every word written down, or they feel the Hadiths were not researched well enough to depend upon.
A classic one for example (I forget who it was that said this, maybe Abu Huraira), recounts how when someone had asked the Prophet who of his two parents should he love more, he replied "Your Mother", and the man had asked, "and then whom", and the reply was "Your Mother", "and then Whom", "your mother" and when he had asked a fourth, the Prophet replied "Your Father".
So yeah, that's an example of one.
edit edit: Let me just skip to a broader question. You talked about dress, but you didn't really clarify other ways in which Islam perceives women.
What is the Islam view of women in leadership? What is it's view of women within the household?
Well, I'll go ahead and lump these two? As far as I'm aware, the dress tends to be one of the more restrictive things. Women had the right to divorce, and inherit and own property.Besides that, we run a gamut of attitudes backed up by religious reasoning from stay at home, stay with a man, to being able to work. Traditionally, there's a push for gender segregation, but all schools I've gone to other than my university have been co-ed.
I don't think I can be too more specific than that, given there are a billion Muslims. I regularly say that since there's a billion Muslims there's a billion Islams.