Well, I'm only passingly familiar with the Quran, I won't hide that. Is it true, though, that a female witness counts as half of a man's witness in certain courts?
Only in cases where there are more men witnesses. (Reasoning: because a woman's honor is well protected and guarded in islam, unless she is an essential and the only witness, she is given ease and support to bring along another woman with her as women is Islam are not supposed to be somewhere far from home all alone. (this by no means lessens the importance of her witness) . Imagine a system where women never went anywhere alone, it was natural then, that if a crime happened, both of them were called as witness, not because a woman witness is considered weak, but because women find great support in their accomplices and most might even refuse to record a statement if they fear that they'd be involved in a certain case and would have to go all by themselves to the courts, leave their kids behind and record statements for cases they do not want to be involved in.)
[Second reason was to ease her from the burden of having to remember specific details about an incident since it is documented about women that they loose a lot of memory in child birth and while managing a number of kids, it is a natural physical aspect of women, ( and since muslims believe that Allah is all knowing,) it seems quite plausible that God gave one woman witness a chance to re confirm her information with her accomplice woman, so that they both can remind each other lest they forget (part of this is mentioned in the Quran) and in order to avoid the mixing up of key information.
I'm sure quite a few women are very sharp of brains and can recall exact details of an incident, but most common women undergo panic when they experience shock and they hardly notice any details, this is a fact! And since Islamic justice system caters to all segments of the society, the level of ease and accommodation begins from the person having the lowest means to fare well in the world, not the richest or the bestest brains, as is the custom of today's world i.e only the best fare well]
Now, in Cases regarding women and children, and other women , one woman witness is held as one. You obviously haven't understood it well at all, all verses have context and the explanation that you have given is hardly is the one that supports it, where did you even get it from?
I understand that there's an "explanation" for women inheriting less (because the man's supposed to work and take care of the wife, blah blah -- which is misogynistic in itself), but I've not seen an explanation for why women count as half of a witness yet -- if indeed that's what the Quran says.
The explanation of daughters inheriting just half from their fathers, of what a son would, is, that she gets the other half from her husband, simple. So that makes her financial baggage complete. While the same son, since he'd be getting married and spending his share on all his family including an old parent, his wife and his kids, thus his share never remains his own, as his financial needs multiply, he gets a little more since he gets to distribute it among his wife and kids. And since a daughter already gets some from the father and some from the husband, it is entirely hers and she is not bound to even spend it on her family, she can do whatever she wants with it, start a business or support her family, it all depends on her choice. Hope that cleared it a bit.