You can use the xcopy command for copying files and sub-folders. The syntax is:
xcopy source destination /S /H
The /s switch will copy sub-folders, and the /h switch will copy system/hidden files.
NB If you're copying the XP files over, then you need the entire contents of the i386 folder
xcopy d:\i386\*.* c:\i386 /S /H
If you're copying the windows 98 files however, then all you need is the win98 folder (without any sub-folders) so you can use the standard copy command instead if you wish
copy d:\win98\*.* c:\win98
NB d: is the drive letter of the CDROM - this may of course be a different letter on your machine
RE. DOS diagnostics...
Unfortunately that are very few that are not windows based, and most of them cost money. I would suggest you try memtest86 though - this is free, DOS based and very reliable although it will only test the RAM.
Download it from here:
Select the 'download - pre-compiled memtest86 v3.4 installable from Windows & DOS' option.
Once it's downloaded, extract the files and run install.bat.
This will create a bootable floppy disk containing memtest. When you run memtest it performs a number of tests and these will take a while, depending on the amount of ram in the machine (I strongly recommend, if you have more than one stick of ram, then test them individually by removing the rest temporarily)