1] eSATA works as per SATA ie must power off system to eject drive.
Not true. SATA and eSATA, are both hot plug technologies. Power off is not required to physically attach, or detach, either one. In OS/2 you MUST close out the file systems before detaching them (shut down the system). You can attach them, at any time, but in OS/2 you must reboot to get them recognized.
Note that some systems have a physical connector for eSATA, and the BIOS should, automatically, recognize that port as being for eSATA. Other systems may use an adapter (or just a cable) that plugs into a normal SATA connector on the motherboard. In that case, the BIOS should have a setting to tell it that the port is used with eSATA (but that doesn't seem to exist in all cases). In fact, that is only used with operating systems that recognize that eSATA can be plugged in, at any time, so it is irrelevant to OS/2.
I am not familiar with eSATA(p), so I don't know how the connector gets power for the external device. The devices, that I have, all use their own power source.
2] eSATA support was dropped at some point, I do not know when.
Not true. All that was dropped is the built in eSATA connectors. You can still use eSATA devices connected to normal SATA ports (see above).