Sure, Win 3.11 WILL work with your hardware.
PIII 550 MHZ: No problem. The faster your CPU is, the better Win3.11 works.
256 MB RAM: No problem.
10.2 GB HD: No problem. Make one or more FAT32 partitions on this 10GB HD, and install DOS + Win3.x.
SiS 620 Video: No problem. Its Win3.x driver is available from:
http://www.asus.com/pub/asus/misc/vga/620w31.zip
C-Media 8738 Audio: Seems to be OK. Its Win3.x driver is available from:
http://www.soundcard-drivers.com/drivers/11/11388.htm
Modem: What's its model? Is it a WinModem?
CD-ROM should work fine in DOS/Win3.x with correct driver loaded.
"Diskette Drive not working (is it really necessary?)"
Yes, it's necessary if you want to install DOS from floppy disks. Since Win3.x is not an operating system, it can't be installed without DOS, which is the real OS. Of course, DOS Installation CD is also available.
"I want to install it on a second partition....is it possible to make a dual boot with my XP?"
If you want to boot DOS/Win3.x from a second partition, then you need to use a additional boot manager/loader to achieve this. However, it's not necessary. As a matter of fact, it's recommanded that you install DOS and WinXP on the same of a different FAT32 drive from their own installers, so you can select the OS you want to boot from in WinXP's own dual-boot menu when system starts. After DOS is started successfully, install and run Win3.x from DOS. Then it should work. For information on how to install Win3.x from DOS, please read this article:
http://newdos.yginfo.net/msdos71/doskbd1.htm
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Long Live DOS!