Workgroup = small office/home use and pants, domain = awesome, same users/groups/printers/shares controlled centrally
Is this 2003 standard, SBS 2003 or other 2003?
Active directory is the database that essentially holds all the Domain info, users/password/groups etc
The server will only be a DHCP server if set up that role and authorised it, if it detects another dhcp server (your hub) it will stop being a dhcp server until you manually disable the hub being the dhcp server and start the dhcp server service again, or restart the server.
Sounds like you need someone to come in and sort it out tbh otherwise you'll be reading guides for days to grasp what everything is implement it, I'm not saying you're thick it's just there is a load to learn and understand how it all integrates and works together, and what effect certain things have on other things... 'tis a little complex at times
What's your time worth to the company vs what you'd pay for someone to come in and sort it? I would estimate 4-6 hours for the server and depending on how many users you have 1-2 hours per user for migration and a bit of training, maybe more depending on how much you've already setup or broke