I do not know a way of deleting the apple apps like mail.
Restore to factory settings by loading the latest version of ios that your machine will support:
Do a full backup of your device. Twice is best -- cloud and computer.
"You can use iTunes to restore your iPhone, iPad, or iPod touch to factory settings and the latest version of iOS."
http://support.apple.com/kb/HT1414?viewlocale=en_US&locale=en_US
"You can put your iOS device into recovery mode, then restore it using iTunes.:
http://support.apple.com/en-us/HT201263
At last resort you could consider DFU (Device Firmware Update). This could void your warranty.
http://www.imore.com/tip-put-iphone-ipad-dfu-mode
nsdjoey explains how to force a reload of ios
https://discussions.apple.com/thread/7067914