Sketch is not working with Nano perfectly like Mega2560

If I connect sensor with 3v3 of Mega and Common GnD, it still gives me faulty readings...
So after experimenting, I noticed following things...

in Nano board:
if baud rate 115200---with Serialmonitor open-- sensor works but gives faulty readings.
if baud rate is 2400---with Serialmonitor open-- sensor works pefectly....
Any baud rate 2400 or 115200 --- with Serialmonitor close -- Sensor stop working.. (I dont have to upload the code again, I just close the Serialmonitor window and sensor stops working)

I have tried ASCII code on nano...it gives me ASCII table at all the baud rates..

on Nano board:
LED blink command with delay...Without serialmonitor it works perfectly, with serialmonitor opened, it just turned on.

LED blink without delay ... Without Serialmonitor it works perfectly, with serial monitor it blinks but Slow....

and in my program, I am using total 110 ms delay which is the requirement from sensor to work and get the reading...
and I also use total 4 counters...and everytime I change the baud rate, counter timing also changes...

is there an issue with uC Timer!?..