With respect to these kinds of discussions, I often find that there are two kinds of "problems" (in quotes, because I don't agree that both are truly problematic):

Problem Type 1 is where women are discriminated against, by law, such that they cannot do something. For instance, imagine a law that says that "women cannot hop on one foot."

Problem Type 2 is where women choose, or do not choose, to do something. For instance, imagine that women are allowed to hop on one foot... and then we find that they do not do it, regardless.

I am all for addressing and resolving Problem Type 1, but I do not believe that Problem Type 2 is actually a problem.

I do not know to what extent perceived sexual differences are based in biology or are "socially constructed" as gender, etc., and I've seen enough argument over the years to conclude that this is not yet settled science. Regardless, we all face social pressure to do things or not to do things, to be certain ways, avoid others, and it is the role of an individual to assess such things and plot their own course, accordingly. So long as women are free to pursue whatsoever they'd like, live howsoever they'd like -- as they absolutely should be -- then I don't think we are further qualified to determine what they ought to pursue or how they ought to live, or what choices are good or bad for them to make. The only person so empowered in every case, in every unique situation, is the individual woman herself, who needs to live with the results.

There is always room for progress. But in the West women have by far the most freedom to be who they want to be. They are still very much second class citizens in other regions of the world, regulated to mass child bearing and little else.

Hadn't seen all that data yet. Nice find!

We've seen a lot of progress on the political representation front here in the U.S. for women since Trump's election, led by Democratic women. This article seems to suggest that the outcome of the 2018 midterm elections, which saw the biggest single-election leap in female representation in our government since 1992, almost entirely because of victories for Democratic women, has inspired the Republicans to respond with women's support groups analogous to Emily's List of their own, which are yielding results already. It goes to show the impact of women seeing other women winning, even from the other side of the aisle! Political victories for women encourage more women to run...in both parties! Which is, incidentally, the intrinsic merit I see in electing a female president. Or even just a female vice president. Doing so will tend to inspire more women, regardless of party affiliation, to run for public office at all levels in the future.

Out of the four metrics the World Economic Forum uses to gauge the relative equality of men and women in their annual Global Gender Gap reports -- health and survival, educational attainment, political empowerment, and economic participation and opportunity -- governmental representation is the single weakest area worldwide overall, and the United States is behind that world average. Overall worldwide, 25.2% of lower-house parliamentary seats were held by women as of the end of 2019, for example, while 23.4% of those seats in the United States House of Representatives are held by women, for example. In a world-historic sense, I think the fact that this is the metric that women are farthest away from equality in overall is probably the reason why it's the gap that's closing the fastest at the moment.

Okay, so let's go through this:

Taking the situation in my country as an example, here you can see the month-by-month unemployment rates for men and women respectively over the last year in the U.S. As you can see, the unemployment rate for women had been marginally lower than that of men (about 0.1 or 0.2% lower typically) before the pandemic hit. But look at when happens beginning in March and April: corresponding to the onset of covid-related restrictions and lockdowns, the jobless rate surges...but that of women rises distinctly faster, reaching a peak of 16.2% at the height of the lockdowns in April, compared to a high of 13.5% for men at the same time. You won't be surprised to learn that it was mostly service type jobs that were eliminated and that most of those were/are held by women. Also, schools were closed down and 76% of our teachers are women, child care facilities were closed and 95% of child care workers in the U.S. are women, etc. Anyway, as you can also see, the jobs market has improved since April, but even now, in the jobs report for August, women's unemployment rate is still a little higher than men's even today. The internet has come to describe the pandemic-induced crisis of this year resultantly as a "she-cession".

To your other queries/challenges:

-I don't know what the situation is over in Ireland, but here in the U.S., women were already about twice as likely as men to be diagnosed with depression, and what's more the mental health gap between men and women in this country increased by about 66% during the lockdown period.

-Aligning with this reality, women are more likely to attempt suicide than men overall, including here in the U.S. Women just use less reliable methods (e.g. are less likely to own firearms, for example). Don't worry though, the younger generation is leading a new trend toward equality of the sexes in successful suicides, as today's girls are succeeding more often in their attempts to kill themselves.

-Concerning child custody matters, I've seen lots of conflicting data, but I don't see any actual evidence to suggest that women have an advantage in child custody predeedings. Notably though, there is evidence that men win up to 70% of child custody cases that they bother to contest and are even more likely to win if accused of sexual abuse. Here's a guy who was convicted of raping his daughter and yet somehow won joint custody of her child!

Bottom Line: it's not easy to find areas of life where women are meaningfully advantaged over men.

There is no practical difference between:

"Women occupy jobs which pay less"

and

"Jobs which pay less are occupied by women"

Please clarify why you think these are different...as the consequences are entirely indistinct.

The difference is, that this has set the base. Women aren't actively seeking out jobs that pay less (why should they). They seek out jobs that women made since long times, and these jobs are paid less. A job like nurse is very important for us as society and it is not understandable why it is paid that badly. Historically this job was filled by nuns, for no pay at all.

The right of white women to vote unchallenged was given 100 years ago*.

And where i live nurses get paid above average as a starting minimum and with some extra schooling they can get up to 3500 euros.

I have no idea about the situation in America and considering how much healthcare cost there they have no valid excuse paying them less.

Hmm check this link,if that's true they get good payment.

https://nightingale.edu/blog/nurse-salary-by-state/

Nurses do well. Even starting out they are making 50k. Nurse Practitioners make 6 figures easy.

Supply and demand governs the economy of the job market. The more specialized the skills, the fewer candidates tend to be in that pool.

Male nurses exist by the way...

Ever hear of a waitress? They get paid shit. And deservedly so.  Who should get paid more - the waitress or the cook? Which one is more skilled?

Also, the waitress gets tips....Do you thing she shares them with the cook?