Thanks for the responses and points you are making.
On a few points mentioned:
If my partner was a single woman without children, of course the situation would be totally different. We would have far more freedom to have a spontaneous life together, travel, be very flexible in our lifestyle, have more vibrant social lives, with no responsibility for anyone but ourselves. I also imagine we would be living together or at least spending many nights at each other's places.
If she had children 4-5 years of age, I doubt very much we'd be in a relationship. I would not be prepared to accept such responsibility, nor the necessary changes to my lifestyle.
So the current situation is somewhere in between - and perhaps we're waiting until the kids reach 18 (as Shibui suggested). Once that happens, we can begin having a more "single" life together. However, this being Japan, kids unfortunately tend not to leave home until many years after 18...this worries me.
Yes, my questions here are purely about the financial/taxation/etc implications of being married. Not about the style of our relationship or any moral viewpoint on the meaning of marriage.
I am like a friend to the children, although because of the language gap (they've spent all their lives in Japan, while my Japanese is not up to understanding what Japanese teenagers are usually saying), I simply try to help and encourage them however I can.