For DOL/Across the line starting of 3phase induction motors, if starting current with load is x times FLC, will the no-load starting current too will be x times the no-load current?.

Hi Mr.sripadmanaban.
The actual starting current is a function of the motor design, and the terminal voltage, and is totally independent of the motor load. The motor load will affect the time taken for the motor to accelerate to full speed and therefore the duration of the high starting current, but not the magnitude of the starting current.

It depends on the load type. If the load is a pump or fan, which is a variable torque load, the motor starts rotation in a no load state, and load torque increases as the speed increases. So for that example, the intial inrush current is always during a no load state.

Mostafa is right.
Until the motor starts rotating, it has no way of "knowing" if it is connected to any mechanical load.
The load, and the type of load can only determine how quickly the inrush current will be reduced towards the stationary load current for the actual load.