No, PS2ESDL does not require such a folder as PS2ESDL on the root of your disk if you don't use PS2DCDMP or PS2ESDL's native game format.
Playstation 3 consoles are not supported by PS2ESDL and will freeze upon launching PS2ESDL.
If you used the traditional USBExtreme game format (Installed by USBUtil, ul_install, ui_install etc.), the games should remain in the root folder of your disk. Do NOT move them around.
Does your USB HDD unit require an external power source? Have you tried unplugging and re-connecting the USB HDD unit?
The disk must be FAT32 formatted, and should not have filesystem errors.
How large is your disk? It seems like there is a problem with getting 1TB+ USB disks to work with PS2ESDL.
The games must all be totally defragmented too, otherwise you will probably not be able to play them even if PS2ESDL detects your USB device.
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