From which rom to which rom?

You mean Jkay?

you can use JKay for any samsung based rom, cause it has it's own unique framework over write

Stock + Custom kernel like siyah..

You need to find out what cause it.. many reasons like apps you installed. since you plan to flash custom I proposed you rooted it any freeze bloatware or find out what slow your device...

1. Using basic way, go to settings -> Applications manager -> under download force close all apps that you hardly use

2. Using basic way, go to settings -> Applications manager -> under all disable all apps that you don't use.

3. user batterbatterystate to check waaklock apps.

Could be some systems apps corrupted what you can do if not too hassle:-

1. Backup all your needed things, go to recovery wipe cache first if still cannot do wipe cache and factory reset
2. Otherwise download your ROM from sammobile and use PC ODIN to flash ROM again.

try Carbon rom
http://goo.im/devs/carbon/i9300/nightly/CA...35631-i9300.zip
its just soo dam  m smooth compare to touchwiz rom

thx for our fren here suggesting me this rom

hold power button
else remove battery

Increase the System Sound volume and see.

S3 volume level is quite low. You need to root the phone and use custom kernel that can adjust the audio volume level.

Can..as long as your phone can be charged..no problem.
But some USB cable give a low current..meaning your phone will be charge slower.