Welcome to Android Central! For the Moto E, you're encountering Google's Factory Reset Protection. If a phone is factory reset without first properly removing the Google account, that's considered an unauthorized factory reset, which then requires the user to input the Google username and password of the account that was associated with the phone just prior to the reset. Did you get the phone used from somewhere? If so, you'll need to locate the previous owner and ask if them to help you log in using their account so that you can properly remove their account, thus allowing you to perform an authorized factory reset. If you can't locate the previous owner, then unfortunately the phone is useless. We can't help you bypass Google's security features.
For the Coolpad, does the problem persist after a reboot? How about in Safe Mode?
https://support.t-mobile.com/docs/DOC-31206. If the problem persists in Safe Mode, then it's most likely a hardware defect. Bring it back to the store to get a replacement, or contact the manufacturer, since it should still be under warranty.