My Moto E hangs if I use some web based apps and other high configured apps. Its screen freezes and it even powers off by itself. What should I do to solve this problem.
Since your device fully power cycles or powers off the only thing I can think of which may help is a factory reset because whatever is happening effects the entire phones operating system.
Also, the problem may just be that the 1GB RAM the Moto E has is not enough to run the apps you want.
Go to Setting- security option-tick off the power button instantly locks and disable any screenlock
Moto E - Service & Repair
Power cycle and check app
•Try power cycling the phone
•Check the Play Store for any application updates.
Try restarting the device
When this occurs, the phone will re-establish connection to network.
1. Hold down the power button until you receive a menu.
2. Touch Power off
3. Press and hold the power key to turn back on
4. Attempt to relaunch the browser
you can do hard reset (backup files first)