1) What modules support PATA host controllers?
2) SATA host controllers?
It depends on the kernel version. For recent kernels PATA and SATA controllers are supported through the 'libsata', but you can still use the deprecated "ATA/ATAPI/MFM/RLL support", module is named "ide".
For me, I use libsata to support SATA and ATA devices, and I never have any problem.