InDesign files don't show in Finder, but open fine from within InDesign itself

When I save a file from InDesign on my Mac, it seems to save normally. If I go to Finder, the files are nowhere to be found. If I go back to InDesign and reopen the files, they open just fine. I'm also accumulating an enormous number of ~file_name_randomnumbers.idlk files each time I use InDesign. These files can't be deleted, even long after InDesign is closed, and get a "the operation can't be completed because one or more required items can't be found (Error Code -43)"

I know there's nothing wrong with my file system since every other application, including Dreamweaver and PhotoShop, are saving files just fine and not leaving remnant files scattered all over.

Needless to say, I'm a bit paranoid about losing my work in InDesign and, worse, I have no way to share these files with teammates other than saving them as PDFs which is far from ideal.

Please advise!