I have 2 questions....

1) After I put my car into park and push the emergency brake in I hear the car make like grinding noise as if the brakes are settling in. What is this noise I hear?

2) Now, I am able to push the car backwards with my hand a few inches and then it locks up. Is this normal?

1) Don't know. Have someone else apply, release and apply the E brake as you work your way around the car to find where the noise is coming from.

2) If you mean with the car in park and the E Brake off, yes you can push your car back a couple of inches and then it will lock up. That is just play in the drivetrain. If the E brake is applied and you can push it back, your E brake is not adjusted properly.

Check the cable that goes to the ebrake. You may have a tear somewhere on the cable shield and the cable has gotten dirty or rusted. Next pull the tires off and check the ebrake lever.

I think the two are related. You have a ebrake caliper lever that'* hanging up. Give the entire brake system a look over.

Where is the ebrake lever?

Also, how often should you flush your brake lines? I have the car with 130k and I don't ever think the lines were flushed.