I wouldn't expect XP to be compatable with W95/98 games, since XP and 9x are completely different operating systems.
Sometimes. Most Windows 9x games can be made to work eventually.
This makes no sense. You don't expect them to work, even though most of them do work? 
How does it not make sense? I don't expect older Win95 games to work in XP. Just because, more often than not, they can be made to work doesn't mean I expect them to.
Take Total Annihilation for example. It's an older game that, off install, will not work in an XP environment. An updated patch is required. This is a game that 'can be made to work' relatively easily, thankfully. But I would not expect a game of its age to, by default, natively run in XP.
Go back even further. Look at pre-win95 games. A lot of those older DOS games were designed to run as fast as possible instead of keep a constant tic rate, and thus run far to quickly in Windows. They can be made to work properly -but I don't install a 15 year old game and expect it to work 100%.
There are no major inherent differences between the 32-bit programs and XP can run those fine without using NTVDM or anything like that. In fact, I have never seen a "native" XP program.
I believe I stated something about 16-bit and 8-bit programs earlier.
I've also had problems where older games don't detect modern RAM or SATA hard drives.
There are some old games that don't see the full amount of memory, but it's usually irrelevant since they would never use all of it anyway. They are still detecting more than they actually need. As for the SATA drives, what game does that occur in? That shouldn't really be an issue in Windows games, since they see the drives only through the OS.
TIE Fighter always gives me a stack overflow error, which is the error that program kicks out when it doesn't have enough memory.
You seem to be assuming I'm 100% talking about windows native games. Some of us still have games around from the DOS days

. DOS programs sometimes used the BIOS instead of the operating system for hardware identification. Anyone who has tried to get sound in an old DOS game running a soundcard with an IRQ higher than 7 has probably encountered some difficulty with it. This is because the BIOS (or at least older BIOS's) didn't assign sound devices with IRQ's greater than 7. When Windows boots, it reassigns the address to something higher that most DOS programs (or even some Windows 95 programs -the original Dark Forces comes to mind) can't recognise.
I've had issues with some older BIOS chips and SATA detection. Since some DOS programs look for the BIOS address ranges, they won't see the SATA drives. Haven't had this issue with newer BIOS chips, but then again I don't try and run DOS programs natively either. I had this issue a couple of years ago, but I can't remember what game it was.