It’s a mix of issues popping up at different times. There were women’s sections made to both encourage women to play chess and to keep sexist men happily segregated. Ability never came into it, though.

There are general tournaments and then womens tournaments. The pro women’s chess field is a bit weaker in strength than the mens, most likely due to them being a smaller fraction of total chess players for many reasons. Womens’s chess also has its own set of titles that only women can qualify for. Both these tournaments and titles can be seen as good for women’s chess since the prize money they win keeps them in the profession and titles allow them to get sponsorships and teaching gigs.

Some women refuse to accept the women’s titles and some people call for the abolishment of women’s sections citing that it does more harm than good for women’s chess.

Not that I am aware of, except for age-old sexism and preferential treatment of male chess players at every step of the way. Chess grandmaster Judit Polgár is the living example of that IMO, simply because her parents circumvented the traditional obstacles for women in chess and thus allowed their daughter to rise to the very heights of chess.

Mostly to encourage more women to play. There’s like an order of magnitude difference in the gender ratio and if it’s a goal to encourage more women to play, you’ll need to create opportunities for them to succeed. It’s always been a political decision.