Can I turn on a iPhone with bad ESN?

I have bought a iPhone from my friend (sprint company) and she reported it lost but got it back. So can I turn the phone on?

No, she would have to do it since it was hers. Nothing you can do otherwise.

So the way this will work is when you wish to turn this on or use it with sprint they will see a flag for the stolen/lost phone and ask you where you got it from. This will go 1 of 2 ways. They will ask you who was the original owner of the device and you can provide them with the proper name (of the account holder it was under) and they may release the phone for use then or they will reach out and contact the person it belonged to while your on the phone or on hold and ask them to verify the phone was recovered. The proper thing to do was for your Friend to call back in and tell them the phone was found and they would unflag it from stolen.