Detecting a 2.8ms pulse using a Arduino Uno
First, better to see whole source and schematics.

"Why is the pin 2 not detecting"

Check:
1. Hall sensor connected to Pin 2


pulses variable declared as volatile.
Check if internal pull up resistor setup consistent with hall sensor connection.
Check that Hall sensor's lowest signal voltage is below 0.3 VCC (you said 5V, so it should drop below 1.5V), BTW 580 - the lowest analog value you showed means 2.83V
Check you are not using nointerrupt();


"Is it possible to gauge anything from Analog read function? Am "

Yes. 
Analog read takes about 0.1 ms in default setup, so should make at least 1000 reads per second to catch peak. 

So, 
Easiest way is to choose some value like 600, when analog read is above mark it as Rising when it drops below mark is Falling.
More complicated ways will include some training and hysteresis to improve detection.

Also I suggest to use voltage limiter instead of voltage divider. This gives better detection.