You could end the first sentence with a period. And start the second with "Furthermore/In addition".
The first sentence is taking about "music" being a means of expressing emotions. The second sentence is talking about the intended purpose of music (as some believe it).
Or you could drop the "and", like Mr. J.R suggested, and use the semicolon.
You are correct that the sentence:
The new pair of scissors I have purchased are blunt.
is grammatically correct. You are also correct that it is an elision, or shortening of
The new pair of scissors that I have purchased are blunt.
The general principle is that modern English permits such elision whenever the result is clear and not ambiguous. Long ...
"Me either" should be slapped out of someone's mouth, if using the same way as "me neither".
It may be more common in some places than in others, but that doesn't make it correct, OR acceptable!
The comma example would be an acceptable exception; even though it would still sound weird.
"Would you like a Coke or a Pepsi?"
I can't see anything wrong with the sentence as it is written.
There is no time gap implied.
It is saying that, at the time time (instant) that the namaz began, women began to outnumber men.
It also implies that, up to the start of the namaz, numbers of men and women were about equal.
Does that help?