I don't use Mandriva so I can't tell you in detail how to proceed, but until someone who does comes along I may be able to give you come hints.
Firstly, there are three ways to control a broadcom 4318.
There is the new b43 driver included in some distributions which works very well with my 4318 but does not appear to be included in Mandriva.
I say 'does not appear to be included' because in your post #5 the output mentions the bcm43xx which was the previous driver and which I and a lot of people could never get to work with the 4318.
There is ndiswrapper which now appears to be your best bet.
If you go the ndiswrapper route then you will need to stop the bcm43xx from loading.
The usual way to stop that happening would be to add two lines to the file /etc/modprobe.d/blacklist-mdv
You can soon see if that has been successful by running the command:
You will need access to the bcmwl5.inf and bcmwl5.sys files from you Windows wireless driver.
Open the Mandriva Control Centre - Network and Internet - Set up a new Network Interface - wireless, and you should have an option to select use a windows driver with ndiswrapper. Point it at your .inf file.
I've checked the various parts are in Mandriva even if I haven't used them to install. I did use PCLOS a while ago which borrows heavily from the Mandriva layout though and it worked easily there.
Hope that helps to get you on the road.