Can't play a songs because "original file could not be found"

See Make a split library portable - Apple Community for some background on iTunes library structure. Apart form specific manipulations mentioned there moving iTunes content around by hand can cause problems. When you say the missing songs are where they are supposed to be, are they at the paths shown on the file tab of Get Info, and are permissions such that iTunes can see and play the files?

NAS stands for Network Attached Storage. iTunes has been known to lose files when rearranging content on NAS. I just wanted to rule that out as a possibility.

If you use iTunes Match or Apple Music then iTunes will attempt to "match" your tracks with content in the store. It is often successful, but might occasionally mismatch an explicit song with a clean version for example. If it cannot match then it will "upload" your copy which it can then provide to your other libraries or devices. See About iCloud Music Library icons and status - Apple Support for more on the status terms.

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Is there a full backup of the library anywhere? Is the media stored on NAS? See About iCloud Music Library icons and status - Apple Support. Apple Music may be revealing earlier damage to the library, since it will attempt to reconcile all of the content in it. Normally iTunes can contain missing tracks which it only mentions when you try to play or transfer them.

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Files with a trailing suffix are likely to be the result of having made duplicates at some point, and then removing the original file when cleaning up. Depending on how many there are you could try manually fixing the file names before another locate operation.

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