I’m very confused about what the actual problem is because the terminology between “playlist” and “timeline” is a little loose. Exporting usually isn’t done from a playlist, but rather from the timeline. Is the timeline what is failing to preview? If it is the timeline being exported, then the contents of the playlist is not referenced and is completely immaterial.
Regardless, it sounds like the source videos are not in the location specified in the .mlt file. A quick way to verify this is to open the .mlt file in a text editor (even Notepad will work) and search for “resource” and look at the file paths. If a drive letter is embedded in the path (such as “E:\Folder\Video.mp4”) then the source files must be put back in that exact location on the E: drive. If the files are on a USB drive and the drive is given a different drive letter when attached, this would break the project. Use Disk Management to change the drive letter, or edit the .mlt file to point to the new drive letter. (Make a backup first of course.)
Read the section on “Absolute vs Relative File Names” in the Documentation for more info: