Drive mode will be retained in DeepSleep mode. For hibernate mode, drive mode should be re-initialized after wakeup from hibernate mode.
No. The SCB SPI does not support QSPI mode. CYT4B devices have another block, called SMIF, to support serial memory interface (HyperBus™, Dual SPI, Quad SPI, and Octal SPI). SMIF is an independent block apart from SCB, available on CYT4B devices but not on CYT2B devices.
The maximum clock speed for master mode is 12.5 MHz. For slave mode, the MISO output goes through different logic paths with different delays for external clock and internal clock driving mode. Therefore, the maximum clock speed for slave mode is 10 MHz (IMO) and 12.5 MHz (External clock).