Well, my english is not too good , so i did not understan your last part question but i will try to give some answer to your questions
Do muslim woman enjoy equal right as men?
In islam man and woman both have equal rights but not similar. In some cases man have some upper hand and in some women. I think yo ask this because you might have many misconcept about this.
Evently if you read the actual concept in some point which you think are degrading women are acutally uplifting women more then man for example its was commonly ask that "Why is a woman’s share of the inherited wealth only half that of a man?" if you actually go to depth of this theory you will inshallallah agree that women actually inherits more see this link for more detial
http://islam-faq.blogspot.com/2009/0...ed-wealth.html
Why are women not allowed to go to mosques?
Who said you that women are not allowed to go to mosques , they are surely allowed. Actullay they are not necessary to go to mosques like men , if they want they can go , if they donot want it up to them.
But for women its necessary that there must be a seperate place in mosques for women , and normally due to space or some other reason as there is no seperate place in some mosques so women donot go there.
In my area women go to mosque , specially during rumzan and in normal days as it is not necessary for them to go to mosque , usually they do not go to mosque. Simple.
Why men dont wear black Burqa as woman
Its also necessary for men to hide its body but there are different rules for man and women , as i am not getting word in english to describe it properly so i think some body else can describe this.
why dont MEN lower THEIR gaze in modesty" and show respect to "other" woman?Just because men cannot control their pervertness, woman have this responsibilities of covering up their beauties ,are muslim men so dangerous that woman have to hide inside garment?
WELL, Men must have to lower his eyes in respect of women , and if some body dont its his personal attitude and not the teaching of islam.
Due to my poor english i did not understand your last part so sorry i cannot answer this.