I wonder now what the real purpose of NC. I mean, if your ex trying to contact you back after you do it, do you pick up the phone or what?? Is it best not to have any kind of relationship with your ex forever or..?

The idea behind no contact is to give you time to get over your ex. If you stay in contact it makes it harder, if not impossible. I say stick with no contact, which means, no, don't pick up

The more "contact" you have the longer it drags on, and the easier the ex can toy with your feelings and emotions just for the heck of it.
And it often gives you false hope.

NC helps you move on easier.
And it means NO CONTACT, delete the emails, text messages and don't answer their calls.