automatic submersible pump actuation project
2. Motor current is around 250 mA. Is this circuit OK for the inrush current of the motor? I'd given the max value of i/p caps - is that OK?
Diodes should take care of that. I don't know what i/p caps means.
3. Is a reverse protection diode necessary at the power input side here? I'm powering the board using a DC jack and if I use a diode then there's a diode drop I've got to allow for in ADC calculations.

During normal operation, the diode drops its typical ~0.6 V. That could be a significant portion of the supply voltage, and as the battery voltage decreases the device may stop working prematurely.
Any component that has a voltage drop across it and current flowing through it is consuming power. If that dissipated energy comes from a battery, the diode is reducing battery life. This may not be an acceptable trade-off in devices that have very low risk of experiencing reverse polarity.

https://www.allaboutcircuits.com/technical-articles/how-to-protect-your-circuits-using-only-a-diode
So is there a low risk of reverse polarity? I would follow the recommendations of the part datasheets and whatever guide you're modeling after.
6. Overall circuit
It's hard to say. Again, I would have to analyze each datasheet for each part... which I suppose I can do:

ATMEGA328P


Oscillator looks good. I'm not sure how the other capacitors attached to the microcontroller fit in.


Ultrasonic sensor pinout and bypass cap looks good.



Other smaller circuits look functional.


Related

https://www.electroschematics.com/smart-water-tank-pump-switcher/