1) I believe the SI3114 card needs PCI 2.2, so probably won't work. I've run a Promise SATA150-TX2Plus in a P100 system with i430TX, which supports PCI 2.1.
2) SATA is backwards-compatible, so yes.
3) I've not even been able to get an 8GB SSD working under 6.22. Fdisk correctly recognizes its size, but can do max 2GB partitions. So far so good, but the boot record doesn't seem to get written correctly so the system can't boot from it.
4) If you have the boot options to boot from different SATA drives, then yes. However I've not seen that option... however you don't need to do multiboot on different drives, you can have multiple OSs in different partitions on the same disk.
Tbh though, in a system this old/slow I'd not bother with a PCI SATA card, instead I'd just go with PATA-SATA adapters. Yes, 150MBps SATA (limited by PCI bandwidth of about 90MBps) is faster than 33MBps PATA, but with a CPU like this, you won't notice the difference. The advantage is much faster boot times (SATA BIOS initialization takes a while), better integration in boot options (if your BIOS lets you choose between C: and D:, you can use two SSDs as you want) and in the case of Win9x and NT less hassle with drivers (i.e. 'it just works'). Save the SATA150 TX4 for a P3-class system.