I've been using s3 for like, almost a year, around 9- 12 months, it happens long ago that my battery keep on draining very fast and charge extremely slow, when i say slow, it means real slow, charged for more than 24 hours, battery 48%, when im using without charging, even when im not playing games, the battery drain for so fast, from 48% to 44% in 5-10 minutes, just surfing webs and whatsapp that's all.

So what i wanted to ask is:
1. Im using Custom ROM, if i go to samsung center and ask them to check what is wrong with my phone, will they be able to check for me since my phone is rooted? If yes, will they charge any fees for that? i mean just checking and identify the problem of my phone, whether it's the battery problem, or the charger problem or the charger's USB problem or the rooted issues, or whatever problem it is, will they charge extra just for that?

2. Could it possibly be my battery problem? I've never change the battery since i bought this phone, from what i heard, normal battery life for every phones is 2 years, isn't it?

3. Before this, i had the same problem too, so i bought an original charger, bought it from samsung center, RM 109, 10W charger, at first everything backs to normal, the phone charge in an extremely fast speed, takes around 3-4 hours from 0-100%, so recently, this slow charging problem came back again, and it's proven that it is not my charger problem anymore, cause i've used my brother's charger and still, still charge that slow.So it could be at first it was my charger problem, then after i change charger, my battery spoil again, cause when i change charger, my phone able to charge in a normal speed, just recently it happens again.

I've been using the same ROM for the past 5-6 months and still stuck in android 4.1 cause of my laziness, really too lazy to change ROM and keep updating my phone since the ROM is so stable.

Anyone tried this ROM before, it's quite famous
http://forum.xda-developers.com/showthread.php?t=2354859 i would like to have your opinion on this

Also i would like to hear various suggestion from all the android masters here. I know there is no best rom that's why my preference is simple. I prefer ROM which gives variety of customization options, i don't really care about battery life as i can bring along charger with me anytime, also lag once a while is okay.