The basic data rate is 200MB/s for SD/MMC cards using 4 parallel lanes and 416Mbps for MMC using 8 parallel lanes
Yes, P2010/P2020 is handled as a block device and it does single or multi-block read/writes. This is handled by internal logic and is set up via the eSDHC register set through the drivers.
Yes, eSDHC interface does support a SDHC card above 4GB. The eMMC standard is introduced in JESD84-A44. The new features of the eMMC that eSDHC does not support, are not supported. However, the basic operation of the MMC card is supported.