Subnetting questions

I have a couple of questions that I have not been able to find definative answers to.
What problems are there with subnetting an existing network.

Can the different subnets use the same gateway?

Can I subnet my existing Windows 2000 network and use my existing equipment,routers,servers.

How would you set up DHCP with the subnet?

How exactly does subnetting benifit a newtork?

I am puting a high point value in hopes of geting all the questions answered