Re: broadcom-wl seems to cause crashes
First, I have no idea why the system crashes. Sorry.
Next, I used ndiswrapper for a long time before any Broadcom drivers for Linux existed. It worked fine for me. But you should be using a Windows driver that makes your device work in XP or W2K or even W98. Drivers for Vista and later are known not to do well with ndiswrapper. Also be sure to use 64-bit Windows drivers for a 64-bit Fedora system. Lastly, be prepared to recompile ndiswrapper for each new kernel (if you're compiling it). If you're using the RPM Fusion kmod version, update that for every new kernel. Otherwise, everything else that I know about ndiswrapper is in that HOWTO that you mentioned.
But what about this... Maybe NetworkManager is the problem. It's not hard to disable NM and establish a connection the old fashioned way with network, ifconfig, wpa_supplicant, and dhclient (I did it that way before I ever heard of NM). Just as a test, you know?
What about the encryption? Try connecting without encryption just for a while to see what happens. Or, try another WPA mode or something.
What about your router? Try connecting directly to the modem for a while.
Things like that might be interesting to rule out at least.