Note - all of these older games use cd-rom based copy protection, which is an issue for Windows 10, which won't allow drivers for the older copy protection schemes to be installed, since it considers those type of drivers in general to be a potential security risk. For Windows 8 or older systems, there's some way to install the needed security drivers, but I'm not aware of the details to do this.
The servers for MW 2005, U1, and U2 were shut down long ago, and apparently the ability to register most EA games made prior to 2008 is gone (there was an older (pre 2008) version of EA account / EA nation, but the URL's for the old EA account web site no longer work). The one exception for NFS games prior to 2008 is NFS Carbon, as the servers are still running, and creating a new online account requires a new (unused) cd-key.
I don't know what the rules are for selling used copies of old EA / NFS games, but if you buy through a service like Amazon, you should be able to get your money back if there is an issue, especially if it's a fulfillment by Amazon seller.
Note that there is a "black edition" for MW 2005. It includes a DVD with videos, and some additional game content. Do a web search for Need For Speed Most Wanted Black Edition for details.
Thank you for your answers. I asked some friends and one of them found his old, nearly forgotten NFS Underground 2 copy. Unfortunately, as @rcgldr said, I couldn't run this game on Windows 10 (same problem) and will probably have to give up.
I loved these 3 games from the NFS series (and 2000 Porsche edition) and would love to be able to play them again.
