However, are they allowed to compete in other tournaments, too?
How high is the price money in female tournaments?
Is there a seperate insei system/pro exam for women?
In HnG we see female inseis and women playing in normal tournaments, is this accurate?
What's the female/male pro ratio?
Who are the currently strongest female professionals?
How do they compare to their male counterparts?

The strongest female pro is without a doubt Rui Naiwei.

While at one point you wouldn't have much of an argument, nowadays I don't think that case can be made so easily.

While at one point you wouldn't have much of an argument, nowadays I don't think that case can be made so easily.

How high is the price money in female tournaments?

Or does anyone know of some young talent that could do that in the future?

My guess would be Xie Yimin. She is by far the best female player in Japan, holding all three major women's titles, and having acquired each without a loss. It is not clear how strong she really is.

The strongest female pro is without a doubt Rui Naiwei.
Here is the livejournal of Cho Hye Yeon 9p, a corean female pro and regular challenger of Rui Naiwei: http://loveku.livejournal.com/
(Although she has trouble against Rui Naiwei or her male counterparts, I admire her very much. She's very strong among females and not many pros manage to study (something else than go) while still pursuing their career in competition.)
You may find some infos there. Or wou can ask wour questions to her directly.
Cho Hye Yeon 9p is listed as being the 4th women to achieve 9 dan ranking and I think it says a lot.
In Corea female pros have their own insei league and pro exam (I read that on her blog). They also have their own tournaments and titles. This is to promote female go players because they have trouble competing against male top pros. I have no idea what the rate is but there are definitely more male pros than female pros.

What's with the weird spelling for Korea?

Why do we even need to distinguish between male and female players? Surely go is one game where physical differences are irrelevant.

Male and female brains are physically different. Males have more grey stuff than females; females have more white stuff than males. Some gender differences in the brains of fetuses are visible as soon as the 26th week of pregnancy.

By way of comparison - there is a much better biological basis for the claim that the best male tennis player in the world should be stronger than the best female tennis player in the world, than there is for Go. (Not saying that the argument is good or bad in either case - getting into that argument would be a horrible time-sink - just that the latter claim is much more silly than the first.)

And yet somehow female professional tennis produces matches and stories that are every bit as gripping as male professional tennis. And colleges and high schools are able to support amazing tennis teams for both genders. And tennis camps are full of little boys and girls, in equal abundance. And if you want to play a casual game for fun, you can easily find another casual player of either gender around your level.

Anyone who doesn't think that the Go world would be healthier with tennis-levels of mobilization of potential female players is neglecting the fundamentals.