Re: kernal or custom rom issue
ive read kernals and customs rom will improve battery life thanks
That's one of those "everyone knows it, but it's not true" things. Some ROMs are written to be faster, which reduces battery life. Some are written to conserve battery (which could mean a slower-running kernel, among other things). BTW, rooting has absolutely nothing to do with battery drain - it just allows apps to run as the administrator. Some apps can't do what they have to do if they run as a normal user.
First read
Battery University - How to Prolong Lithium-based Batteries If you're like most people, you're probably charging when the phone gets near zero charge, which is killing the longevity of the battery. Constantly discharging until the phone turns off - at around 2% of charge (if you drain a lithium battery to 0, you have toxic waste, not a battery - since charging a fully discharged lithium battery can result in quite a large explosion, the battery disconnects from its terminals before it reaches zero charge) can give you a 6 month battery life. OTOH, my V551 original battery (from about 2004) still gives me almost full life. Charge at the 40%-60% point. If you need more life than that, buy another battery and switch them when the one in the phone gets down to 40%. (An S3 battery is less than $10 - look on Amazon.)
BTW, speed and battery life (time between charges) are a lever balanced on a point - raise one and you lower the other. The faster you run the CPU, the more current it uses. Faster and longer time between charges is like dry liquid water.
If you need REALLY long time between charges and you use the phone a lot, get a huge external battery. There are external batteries that have 10 times the capacity of the S3 internal one.
You might also want to run
Greenify and hibernate all the apps that don't have to run by themselves (like email and phone, to receive incoming stuff as it happens, alarms, etc.) That can save a lot of battery.