That description of Jakarta Airport is either many years out of date, or written by someone who's never actually been there. It doesn't have the most up-to-date facilities, but none of that harrassment stuff ever happened to me there, and I've spent a lot of time there for both domestic and international flights. Also I didn't really study the toilets closely, but although they probably do have squat toilets, they also have the western kind.
I think the stuff about women traveling alone is also bunk -- unless they're foolish enough to follow one of the unauthorized taxi touts instead of going to the official taxi stand, in which case either men or women will have problems.
I think it's generally a bad idea to sleep in airports anyway, unless you can get a day room. Narita Tokyo has great day rooms that are about 15 bux and little bigger than a bed and shower; and Changi airport also has decent, inexpensive day rooms. In both cases you don't have to go through customs to get to them, which is a plus.