Sketch is not working with Nano perfectly like Mega2560

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

That sounds reassuring.

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....

Really? That sounds odd. Did you disconnect everything when you did the blinks?