i have several confusion on how to connect a single battery onto different parts of my robot.
I planned to buy 12V battery from ebay which needs to power several components of my robot.
Since i would like to step down that 12V to 9V,6V and to the arduino itself, do I need to use different voltage regulator for that different step down output?
You can put 12VDC into the arduino but it may heat up the onboard regulator past it's limitations--depending on what loads the Arduino is supplying.
Stepping DC down from 12 to 9 or 6 can be done a few different ways
an LM7809 can provide regulated 9 VDC
an LM7806 can provide regulated 6 VDC
an LM7805 can provide regulated 5 VDC (but i'm not sure if you should but 5 VDC into the arduino as it's onboard regulator may chop that down--these regulators tend to require 2 volts above the regulated value.
I've used these in the past and they work fine--and super simple to install. But are only good for around 1 amp. Depending on the load you will probably need a heat sink. Mine alwasy seem to get pretty warm as efficiency is not that great.
Another approach are buck converters. super high efficiency, need no heat sinks, are adjustable and can provide much higher current. I've started using these and the seem to work very well
There is a comparison between linear voltage converters (eg LS7805) and a buck (step down) converter in my YouTube Channel video #21 - see my signature for the URL.
This may help you understand the differences and advantages of both devices.