Question [Q] Firmware and rooting

Hi all, I've just got my 1st ever Android phone (Galaxy S). It's amazing how flexible and overwhelming the phone and system can be.
I've 2 questions:

1. After installed Kies on my PC, it says there's a firmware update that my phone needs, but on trying to install, it gives all sort of problem, ie: memory full, battery low..etc..
What's the deal here? How do I update the firmware?

2. I've read a little about rooting the phone. How does it work and is it safe? Procedure? Any advice?

Appreciate all your advices..

Thanks all,
DaveL