Hi yk,
No worries about many questions.
A BUSY HI indicates that the AD7895 is converting and goes LO when conversion is complete and this also indicate that the data is available on the output register. After the conversion, which is about 3.8us after /CONVST falling edge, then a 16 SCLK cyles should be applied to read and clock out the serial data beginning with 4 leading zeros then followed by DB11 - DB0.
As indicated on the datasheet, a falling edge of the /CONVST will reset the AD7895 and would return to a known state every conversion. Having a /CONVST falling edge between the 16 SCLK cycles or read operation will reset the data register.
On your second question I need to confirm that, but since it was not mentioned on the datasheet, I think it is not recommended to have a /CONVST falling edge while converting or BUSY is Hi.
If would also be helpful if you can share the snapshot of your signal when it is working and when it is having problem. By the way what is the frequency SCLK and the duty cycle of SCLK?
Regards,
Jonathan