A few answers....
Yes, usually COPYING from a read-only media results in files with the read-only attribute set, unless you specified otherwise in a copy command.
Yes, as far as I know, if you install UT2003 and all the updates you have now, in the same order they were installed, overwriting the saved version should fully restore the game. The only conceivable problem might be if the OS you install to in the future isn't the same, or is patched differently. Even then, it's not certain there would be a problem. I think it is unlikely to go wrong, unless the new OS is substantially different. Also, remember to use the same DirectX should you need to re-install.
Yes, zipping the files, saving the ZIP onto a DVD, then unpacking them onto your system will restore not only the attributes, but the file dates as well.
In both cases you'll need to copy over the files with the same user strength as they were installed in the original system, just to be safe.
Oh, the reason for the greyed out file attributes... When you look at the attributes of many files at once, the system will grey out the attribute if all the files in your selection aren't in the same attribute state. This is no big deal, just click on the greyed attribute anyway, it will become ungrey and in some initial state. If you don't like that state, just click on it again, and you're good to go.
Another way to change the attributes is from the command line command ATTRIB. This will permit you to change multiple files at once, and specify sub-folders too. But alas, that kind of thing (the command line) is passe' nowadays and reserved for us dinosaurs.
Good Luck.
P.S. - Save yourself some trouble and include the contents of your redirect server on the disk too. It will save you having to reconstitute all those compressed files.