will try the 3000mah batt tmrow...will give the feedback on the performance
try app2sd on playstore...

You are over thinking things.

granted it's fair enough to understand you are cautious about rooting because you are afraid of bricking it.

however keep in mind you can easily restore a bricked S3 if you use odin3 to flash back the ori firmware.

Also to brick the phone, you need to be silly enough to disrupt the flashing mid process, or do it when your on low power.

Lots of people have already rooted with no issues.

But if still you are worried then, i don't know how else to convince you, but it's your choice.

Rooting benefits:
1. lots of app options like able to install avast anti virus on root for better protection from thieves who try to remove sim card or delete the app
2. whenever you go overseas, you can simply use the local pre-paid card to have cheap access to phone service without resorting to expensive roaming exorbitant fees
3. other apps like supersu which controls permission rights, require your device being rooted. Lots of other useful apps require root.
4. ability to install custom roms. one of the most impressive is wanamlite which removes the bloatware from the S3, so storage space and resources aren't wasted on junkware that is useless. Not to mention custom roms tend to have features, fixes and tweaks that further improve compared to the original rom.
So this is why you should root 
Google for the youtube guides on how to

1. root your device (there are a few rooting methods. The one i used and recommend is CF-Root + Odin3 )
2. install a custom rom (optional, although i strongly recommend it, specifically with wanamlite which is popular on lowyat)
3. install a custom kernel (optional. some people feel fine using the stock kernel from wanamlite, but others feel siyah's is better for the extra tweaks and features. also keep in mind siyah kernel doesn't support jelly bean if i read this correctly. works for ICS though)
but if you think it's mahfan to google this and watch the youtube guide then i don't recommend it. Rooting isn't for lazy people. Cauz if something go wrong they simply blame others when they never bothered to follow instructions or read easy guide themselves 

This app is a hit n miss affair n will not work for all apps
You just got to try your luck. Older gameloft games maybe

did u start ur game thru gl to sd?
u must start ur game from there

Root and use binder OR buy a 32GB S3