apple macbook pro screen doesn't comeback if we hit a key instantly after it goes to sleep
If the screen is going off at the same time that the system is sleeping, you're likely seeing a delay from the system writing its hibernation files. By default, OS X sets up sleep such that if power fails, the system can restore itself when it's plugged in again.

Generally, I advise against this, but if you wish to experiment with disabling hibernation, use the following command in Terminal:

sudo pmset -a hibernatemode 0

You can restore the normal hibernation mode setting with:

sudo pmset -a hibernatemode 1

If your HDD is low on free space, writing large files will be very slow because of extreme fragmentation. Freeing up disk space can make a significant improvement in performance.

Edited to add:

A workaround for this may be to set your screensaver/display sleep time to be earlier than your system sleep time. Even if it's only by a minute or two, it will change the dynamics of your interaction with the system.