Hello Tak-san,
Thank you for your questions.
1. Yes, you are correct. When a digital reset (Register 0x08 = 0x03 --> 0x00) is invoked, the AD9257 goes into an initialization phase where an internal state machine sets up the biases and the registers for proper operation. This takes about 3M sample clock periods.
Please keep in mind that the 375us wake-up time is the time to wake-up from power-down mode, and not from when the ADC is first powered up.
2. When first powered on the AD9257 goes through the same initialization routine as invoked by digital reset. There is an assumption that the sample clock is stable when the AD9257 is powered up. If this is not the case, and digital reset by Register 0x08 should be performed after power up. This is discussed in the CLOCK STABILITY CONSIDERATIONS section of the datasheet.
3. Yes, you are correct. Digital reset is not needed when changing between DCS-on and DCS-off.
Nevertheless, I think it is good general practice to invoke a digital reset after any change in AD9257 state.
4. The amount of time required for digital reset is the same, regardless of if DCS is enabled or disabled. Is this your question?
I hope your project goes well.
Doug