There is a way I have seen on the internet.
Basically you hit the emergency call button.
Immediately hit the top/power button twice.
It will still be connected to the call. Hit the plus button/add contact.
You should be able to leave to the home screen.
If this doesn't work you can try looking it up on Youtube, trust me it's somewhere on the internet.
You don't. You will have to produce the password---you can get help with password reminders from Apple. If not, you can produce the original receipt.
Outside of that, there are a zillion shady companies out there that will take your money to help you launder a stolen phone. There is no well established long lasting solution--at any time you can lose the activation unlock--if you are able to get one--when Apple updates the iOS.
This really is a dead end.