What part does the CodeWarrior tools that you have target? (HC08, S12, ColdFire...?)
The IDE v4.5 is an old one. If I followed you, you've updated to a later one. The latest Classic IDE is v5.9.1.
The key was a license key. How licensing was handled changed between v4.5 and v5.9.1. It used to be you were given a key number and you entered it. Now you register on-line and the system gives you a license file that you place in your CodeWarrior directory.
To answer your specific questions:
#1: No, lot and part number have nothing to do with a license key.
#2: I haven't tried replacing just the IDE executable, so I don't know what the outcome would be. Because the newer IDE might require other, new files to function properly, I would not recommend that. It would be better to do a complete install.
#3: Choose Help > About CodeWarrior and click on Installed Products. That displays a list of all of the installed tools and their version numbers.
---Tom