Windows

First 1 question:
Why aren't you upgrading directly to windows 2003 server? If you don't you'll be confronted with that in the near future.

Here are some links, anyway:

NT to Win2k:
http://support.microsoft.com/default.aspx?scid=kb;en-us;298107

NT or Win2k to Win2k3:
http://www.microsoft.com/seminar/shared/asp/view.asp?url=/Seminar/en/20030424vcon19/manifest.xml

What do you mean by "schema?"

Did you mean your organizational structure of domains, workstation and computer names?

Active Directory makes logical organization much easier.

I would advise you to move to Windows 2003, as there have been many improvements over Windows 2000, especially in the areas of DFS, AD replication and DNS.

Windows 2003 Unleashed would be a good book to pick up and read if you don't have any experience with implementing Active Directory. And whatever you do, do NOT name your AD DNS namespace the same thing as your external DNS namespace. I make a nice living straightening that kind of mess out!

don't know

maybe this is what you want:
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http://www.microsoft.com/windows2000/downloads/tools/admt/default.asp
The Active Directory Migration Tool provides an easy, security-enhanced, and fast way to migrate to Windows 2000 Active Directory service. As a system administrator, you can use this tool to diagnose any possible problems before starting migration operations to Windows 2000 Server Active Directory. You can then use the task-based wizard to migrate users, groups, and computers; set correct file permissions; and migrate Microsoft Exchange Server mailboxes. The tool's reporting feature allows you to assess the impact of the migration, both before and after move operations.

In many cases, if there is a problem, you can use the rollback features to automatically restore previous structures. The tool also provides support for parallel domains, so you can maintain your existing Windows NT? 4.0 domains while you deploy Windows 2000.

How to download and install
Select your language from the drop-down list at the top of the page and click Go.
Click Windows 2000 Active Directory Migration Tool.
When the File Download dialog box appears, select Save or Save this program to disk.
Choose a location on your computer to save the file, and then click Save.
How to use
Go to the location where you saved the file and double-click admt.exe to launch the Setup Wizard.

How to uninstall
Go to the location where you saved the file and double-click admt.exe.
Click Remove All in the Setup Wizard.
Learn More
Active Directory Migration Tool Overview