Designing of an audio amplifier using LM386 and a preamplifier
But i am still getting acoustic howling. What can I do to prevent it
  dynamically.


I'm going to assume you mean feedback squeal, and you have it if you can stop it by blocking the mic. If that's what you have, you MUST isolate the speaker sound from the microphone. At the least, you point the speaker and the mic in opposite directions. Depending on sensitivities, you may need to put some sort of acoustic shield between the two.


  Also I want to increase the sensitivity to the extent that when I rub
  my fingers in front of the electret mic the speaker should be able to
  play it .


This will just make your feedback worse. Plus, it's not likely that a cheap electret mic will have the dynamic range to sense what you want. 


  also I think that to eliminate the mains noise I need to eliminate the
  ground loops . How do I eliminate ground loop ?


You don't have a ground loop. You're just picking up 60 Hz noise. You need to learn about shielding, not ground loops. As a first step, put both circuits on the same breadboard. It's possible that the big loop of wires which connect the two boards is serving as an antenna. In general, keep all of your leads as short as possible. Plus, as long as you put, say, a 10 uF capacitor (with the other lead to ground) on both the 386 Vcc and the 7805 output you can use a single battery.


  Also Can i use a simple op amp like 741 c to eliminate the noise where
  the inputs are a scaled version of the output and the preamp input


I'm not quite sure what you mean, but you must not, under any circumstances, use a 741 in this circuit. 741s are not well-suited to low power voltage circuits such as your single 9 volt batteries. What do you mean "the noise"? How do you know you have noise? What is it like? Why is it objectionable?