iTunes convert file type errors

Where did the songs come from? You mention "iTunes songs", but what do you mean by that? Are they iTunes Store purchases, or simply music, obtained elsewhere, that you've added to your iTunes Library?

• You cannot convert music from Apple Music, so if the music is from an Apple Music subscription (which is an Apple product), it will not convert
• Songs purchased from the iTunes Store several years ago may have copy protection built in, that prevents conversion. They will be m4p files. More recent purchases, m4a files, do not have that restriction
• Why are you attempting to convert the songs? Modern mp3 players should be able to play m4a files, purchased from the iTunes Store

One possibility is that the files are corrupted in such a way that they play in iTunes (you haven't said that they don't) but they won't convert correctly.

We've definitely seen a problem with faulty downloads from the iTunes Store. The fix for that is to delete the file and download it again. If you can work up the enthusiasm, you could try that and see what happens.

However, after a quick look at MusicBee, I took a longer one instead.

It turns out that in theory, m4a files (also known as aac files) should play in MusicBee, but there are known problems, particularly on Windows 10. MusicBee's Wiki offers a solution (in the form of a free, third-party add-on).

I won't post a link because Apple might think that's a step too far, but I believe my help with your problem is justified since it concerns purchases from the iTunes Store (the songs) - and it would be unreasonable to find that music purchased from the iTunes Store cannot be played outside Apple products. (For the benefit of others reading this, who might wish to comment, Apple Music is not purchased, so the restrictions with that are understandable.)

Sorry that there's not more I can do.