HI, for the glass if you don't use a screen protector i will recommend that you buy if you want a LIQUID SCREEN PROTECTOR like NANOFIXIT. I have apply it on my phone and it's work very great. You can buy it on eBay or Amazon.
Maybe it's because your battery is too HOT? Is your battery is hot when you take your battery out of your phone? And your phone doesn't came HOT before shutting off ? Because when the phone is shutting off itself it's because your battery is too HOT.Install a application who can refresh your battery and maybe you have to many application on your phone and if you can transfer application on your memory card.
this is not a simple issue, you were not supposed to delete apps or refresh your battery in order to properly use your phone. my advice to you is to request a replacement or send to Samsung for analysis. might be a battery problem, falty motherboard or something else.
Hey @Chum, the other members are correct in that you shouldn't be needing to take out your battery in order to get your device to work again. Please contact your local Samsung Service Center (http://www.samsung.com/ca/support) so they can take a look for you!
Hey @unofficialQA, this issue is difficult to diagnose or troubleshoot without physically inspecting your device. As I've also suggested to @Chum, please contact your local Samsung Service Center (http://www.samsung.com/ca/support) so we can help!