Mac Mini '19 finder crashing in Catalina 10.15.2

It's still under warranty, so I would make an appointment at the Apple Genius Bar for service. If you need to find an Apple Store - Find a Store - Apple. Also, see How to find your nearest Apple Authorized Service Provider (AASP) or Distributor (AAD).

"Your Apple-branded or Beats-branded hardware product (“Product”) is warranted against defects in materials and workmanship for a period of ONE (1) YEAR from the date of original retail purchase (“Warranty Period”) when used in accordance with Apple`s user manuals (refer to www.apple.com/support/country). Under this warranty, you will be able to direct your claims to Apple even in situations where you purchased the Apple Product from a third party.” [Apple One (1) Year Limited Warranty – Accessory - For Apple and Beats Branded Products Only.]

If you don't wish to take advantage of your warranty:

A Troubleshooting Procedure that may Fix Problems with macOS El Capitan or Later

You should try each, one at a time, then test to see if the problem is fixed before going on to the next.

    Be sure to backup your files before proceeding if possible.

1. Shutdown the computer, wait 30 seconds, restart the computer.
2. Disconnect all third-party peripherals.
3. Resetting your Mac's PRAM and NVRAM
4. Reset the System Management Controller (SMC)
5. Reset your Startup Disk and Sound preferences, if needed, after resetting the PRAM.
6. Test in safe mode to see if the problem persists, then restart normally.  Use safe mode to isolate issues with your Mac and Playing Safe - what does Safe mode do?
7. Repair the disk by booting from the Recovery HD. Immediately after the chime hold down the Command and R keys until the Utility Menu appears. Choose Disk Utility and click on the Continue button. Select the indented (usually, Macintosh HD) volume entry from the side list.  Click on the First Aid button in the toolbar. Wait for the Done button to appear. Quit Disk Utility and return to the Utility Menu. Restart the computer from the Apple Menu.
8. Repair permissions on the Home folder: Resolve issues caused by changing the permissions of items in your home folder.
9. Create a New User Account Open Users & Groups preferences. Click on the lock icon and enter your Admin password when prompted. On the left under Current User click on the Add [+] button under Login Options. Setup a new Admin user account. Upon completion log out of your current account then log into the new account. If your problems cease, then consider switching to the new account and transferring your files to it - Transferring files from one User Account to another.

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Continued from previous post:

10. Reinstall OS X by booting from the Recovery HD using the Command and R keys. When the Utility Menu appears select Install OS X then click on the Continue button.

11. Erase and Install OS X Restart the computer. Immediately after the chime hold down the Command and R keys until the Apple logo appears. When the Utility Menu appears:

     1. Select Disk Utility from the Utility Menu and click on the Continue button.

     2. When Disk Utility loads select the drive (out-dented entry) from the Device list.

     3. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.

     4. Set the Format type to APFS (for SSDs only) or Mac OS Extended (Journaled.)

     5. Click on the Apply button, then wait for the Done button to activate and click on it.

     6. Quit Disk Utility and return to the Utility Menu.

     7. Select Install OS X and click on the Continue button.

Note: There are no Mac mini 2019 models, the current model was introduced in 2018 and that's the date that is used to identify the current model. It's not the date of your purchase, it's the date of the model's introduction.

No, they won't void your warranty. However, if it is still under warranty, then you may want to let a local Apple shop fix it for you. Use the warranty. That's what it's for.