I can answer a few of those questions for you.
1. Here is a good link that explains the filesystem hierarchy. It is a more abstract explination based on IEEE standards that could be applied to any *NIX based system.
http://www.pathname.com/fhs/pub/fhs-2.2.pdf
As far as installation, most programs should install themselves, in the /usr/local directory, or someother directory in /usr. The danger of installing programs in your home directory (/home) is that other users won't be able to run those programs. Anyway, most programs should come with documentation telling you where to install them, either in the tarball or on their web site.
4. For the most part windowmanagers run very slowly, at least Gnome & KDE, and that's because they are linux's equivalent of windows. I only use Window Maker because for me it's, by far, the fastest, plus I compiled it with KDE & GNOME support, so I can run any app for KDE or GNOME under it. And just so you know, it is not a video problem, but more of a bloatware problem.
The AC97 is supported in the kernel, and I'm suprised that Mandrake didn't automatically detect it during the install. You might have to load the AC97 sound module by hand, or compile a new kernel to get it working. It would be a good idea to install the kernel source, if you haven't done so already.
You mentioned that the documentation wasn't very good. From what I have read on them in the past, they should do a pretty good job helping you get started.
http://www.mandrakelinux.com/en/fdoc.php3
http://www.linux-2000.co.uk/doc/en/mdkuserguide/
And you might want to take a look at this site, it's the mother of all Linux Documentation. Actually, it's The Linux Documentation Project site, you should be able to find docs/man pages/HOWTOs on just about anything that you want to do.
www.tldp.org
All in all, welcome to Linux. I experienced some of your same questions/frustrations the first time I installed & ran Linux (Red Hat) , but the more you experiment around with Linux the more you will learn.