Why is it the battery drains faster when I am in a 3g or 1x service area. The back of the phone gets hot and the battery doesn't last my normal 1.5 - 2 days.
Welcome to Android Central! Probably because the LTE radio is expending extra battery searching for that nonexistent 4G signal. You could try going to Settings>Wireless & Networks, tap More, then Mobile Networks, then Preferred Network Type, and see if you can select 3G only.
Install the "LTE On/Off" app from play store. I use it when I don't need LTE or know I won't get an LTE connection for some time and want to conserve power.