If you want to use 32bit host OS, then you only have one choice - Xen.
Yes... All software is 32 bits
I think he meant if you had a 32bit host to run the guests on, and did not mean 32bit guests. If your hardware has virt extensions, then it's a 64bit host.
KVM certainly runs 32bit and 64bit guests, and it runs linux guests just as well as windows...