SATA to IDE adapters are not all the same.
IMHO, if one buys such an adapter with an unidentified/unbranded chip, he better be feeling very lucky. It might work well, or not at all, or something in between .
Additionally, even known brand chips have their compatibility issues with certain IDE controllers. Adapter design/build issues can be variables too.
The PIIX4E on the P2B-F works fine with JMicron and Marvell based SATA to IDE adapters (at least the ones I have tried). ICH2 works fine with those as well. JMicron based adapters have issues with later (post ICH2) Intel IDE controllers and VIA 686B controllers, however (stability and or DMA, AFAICR).
As for the disk size issue, it can be addressed using XTIDE BIOS, either as an option ROM on an ISA NIC, or a dedicated XTIDE card or even as an option ROM in a modded BIOS, like I have working on my P3B-F Adding XT-IDE option ROM to Asus P3B-F BIOS [Thanks to DenizOezmen, it actually works!!!]