They are all the same kernel.
They all use the same user land apps and daemons.
If you have problem with a device in one distro, you're probably going to have the same problem in others.
Not really, each distro heavily patches the kernel, Mandriva included, and not necessarily with the same patches. Plus as the distros tend not to come out on the same day they also often have different kernel versions. On top of that the userland tools to detect and set up hardware are not the same and things like automating ndiswrapper wifi driver installs tend to be better on Mandriva
I second Mandriva, I've been using it for close to a decade and it is definitely easier to set up than Ubuntu, plus being KDE based will be a bit easier for a Windows user to get used to.
However, there is one caveat, in the last month I have started converting my PCs to OpenSUSE as Mandriva seems to be slowly dying with take-over after take-over and the current 2010.2 version is somewhat long in the tooth.
Mandriva do a live CD which can be also run from a USB disk, why not try that first?