iTunes asks me to authorize my computer every time I try to play my purchased music! AND doesn't want to convert to MP3!!!

Remove download. That should leave you with a cloud icon you can use to redownload. You won't need to pay again.

Repeated requests to authorize an already authorized computer for recent store downloads typically indicates you have corrupt or incomplete copies. Delete the tracks that won't play from your library without hiding from your purchase history. Redownload using the cloud links that should remain, or close iTunes and reopen if they don't show up straight away. While downloading click the activity widget and turn off the option that allows for simultaneous downloads.

If that hasn't helped see If iTunes prompts you to authorize your computer when you try to play iTunes Store purchases - Apple Support.

tt2

Use the second link and relate it to your recent purchase. Phone support is usually limited to hardware, one incident, within 90 days of purchase, unless you pay. Web forms, email, online chat, etc. should all be free but require a little more patience.

tt2

Delete and redownload the songs which won't play. If this isn't free in your country, click here and ask the iTunes Store staff for assistance.

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Yes. See Hide and unhide music, movies, TV shows, audiobooks, and books - Apple Support if you allowed the tracks to be hidden from your purchase history when deleting them.

tt2

Try https://support.apple.com/itunes or for recent purchases use https://reportaproblem.apple.com/.

tt2

You're welcome. 🙂

tt2